Word Problems - GED Math

A water tank is being filled at a constant rate of 12 liters per minute and initially contains 45 liters. Which equation shows the amount of water $W$ in the tank $t$ minutes after the pump starts?
Answer: $W = 45 + 12t$ When you encounter word problems about rates and initial amounts, you're dealing with linear equations where something changes at a constant rate over time. The key is identifying the starting value and how it changes. Let's break down what's happening: the tank starts with 45 liters and gains 12 liters every minute. After $t$ minutes, the tank will contain the original 45 liters plus whatever additional water has been added. Since water is added at 12 liters per minute for $t$ minutes, that's $12t$ liters of additional water. So the total is $W = 45 + 12t$ . Choice A ( $W = 45 + 12t$ ) correctly represents this situation with the initial amount (45) plus the rate of change (12) multiplied by time. Choice B ( $W = 12 - 45t$ ) makes two critical errors: it treats 12 as the starting amount and suggests the tank loses 45 liters per minute, which contradicts the problem stating it's being filled. Choice C ( $W = 45t + 12$ ) switches the roles of the initial amount and rate. This equation suggests starting with 12 liters and adding 45 liters per minute, which doesn't match the given information. Choice D ( $W = 12t - 45$ ) implies the tank starts empty and somehow has 45 liters removed from it, resulting in negative water amounts initially. Study tip: In rate problems, always identify what you start with (the constant term) and what changes over time (the coefficient of $t$ ). The general form is: Final Amount = Initial Amount + (Rate × Time).
A rectangular garden's length is 4 feet more than twice its width. If fencing costs $8 per foot and the total cost to fence the garden is $320, which equation can be used to find the width w of the garden?
Answer: $8[2w + 2(2w + 4)] = 320$ When you see a word problem involving perimeter and cost, you need to work systematically through two key relationships: the geometric constraint and the cost calculation. First, establish the dimensions. The length is "4 feet more than twice the width," so if width = w, then length = 2w + 4. The perimeter of a rectangle is 2(length + width), which gives us 2w + 2(2w + 4). Next, apply the cost constraint. Since fencing costs $8 per foot and the total cost is $320, you multiply the perimeter by the cost per foot: 8 × [2w + 2(2w + 4)] = 320. This matches answer choice B. Looking at the wrong answers: Choice A gives you $2w + 2(2w + 4) = 320$ , which calculates the perimeter in feet but ignores the $8 cost per foot—this would only work if fencing were $1 per foot. Choice C uses $8[w(2w + 4)] = 320$ , which multiplies cost by area (length × width) instead of perimeter—a common mix-up. Choice D gives you $8[w + (2w + 4)] = 320$ , which represents the cost of fencing just the length plus width, forgetting that you need to fence all four sides of the rectangle. For word problems involving perimeter and cost, always remember the two-step process: first find the perimeter formula using the given relationships, then multiply by the unit cost. Don't confuse perimeter (distance around) with area (space inside).
A movie theater sells adult tickets for $12 and student tickets for $8. On Friday night, they sold 150 more adult tickets than student tickets and earned $2,880 in total revenue. Which equation correctly represents this situation if s represents the number of student tickets sold?
Answer: $12(s + 150) + 8s = 2880$ Let s = student tickets. Since they sold 150 more adult tickets than student tickets, adult tickets = s + 150. Revenue = (adult price × adult tickets) + (student price × student tickets) = 12(s + 150) + 8s = 2880. Choice B incorrectly assigns the higher price to student tickets and adds 150 to student tickets instead of adult. Choice C assumes exactly 150 adult tickets were sold. Choice D treats 150 as additional revenue instead of additional tickets.
The population of a town is currently 42,000 and grows by 1,150 people each year. Which equation gives the projected population $P$ after $y$ years?
Answer: $P = 42{,}000 + 1{,}150y$ When you encounter population growth problems, you're dealing with linear growth models. The key is identifying the starting value and the constant rate of change, then building an equation that adds the growth over time to the initial amount. Here, the town starts with 42,000 people and grows by a fixed amount (1,150 people) each year. After 1 year, the population would be 42,000 + 1,150. After 2 years, it would be 42,000 + 2(1,150). After $y$ years, it becomes 42,000 + $y$ (1,150), which gives us $P = 42{,}000 + 1{,}150y$ . Choice A is correct because it properly represents linear growth: starting population plus the yearly increase multiplied by the number of years. Choice B uses exponential growth with $P = 42{,}000(1{,}150)^y$ . This would mean the population multiplies by 1,150 each year rather than adding 1,150 people—a massive and unrealistic growth pattern. Choice C reverses the roles with $P = 1{,}150 + 42{,}000y$ , making the yearly increase only 42,000 people starting from just 1,150. This misidentifies which number represents the initial population versus the growth rate. Choice D shows $P = 42{,}000 - 1{,}150y$ , which represents population decline rather than growth. The subtraction indicates the town loses 1,150 people annually. For linear growth problems, remember the pattern: Final Amount = Starting Amount + (Rate × Time). Always identify what stays constant (starting value) versus what changes over time (rate × time period).
A plumber charges $55 for a service call plus $40 per hour of work. If the total bill was $295, which equation can be solved to find $h$ , the number of hours worked?
Answer: $55 + 40h = 295$ When you encounter word problems about costs with both fixed and variable charges, you need to identify each component and how they combine to create the total cost. Here, the plumber has two cost components: a fixed service call fee of $55 (this happens once regardless of time) and an hourly rate of $40 (this depends on how many hours $h$ are worked). The total cost is the sum of these: fixed cost plus (hourly rate × hours worked) = total bill. This translates to: $55 + 40h = 295$ , which is choice A. The $55 is added once, and $40h$ represents $40 multiplied by however many hours were worked. Choice B ( $55h + 40 = 295$ ) incorrectly makes the service call fee dependent on hours worked and treats the hourly rate as a fixed cost. This reverses the problem setup completely. Choice C ( $40h - 55 = 295$ ) subtracts the service call fee instead of adding it. Since both the service fee and hourly charges are costs the customer pays, they must be added together, not subtracted from each other. Choice D ( $295h = 55 + 40$ ) incorrectly multiplies the total bill by hours, which makes no mathematical sense in this context. The total bill is the result, not a rate. Study tip: In cost problems, always identify what's fixed (happens once) versus what's variable (depends on quantity). Fixed costs get added as constants, while variable costs get multiplied by the quantity, then everything sums to the total.
A savings account has a balance of $1,200 and earns simple interest of 3.5 % per year. Which expression represents the total amount of interest, $I$ , earned after $t$ years?
Answer: $I = 1200(0.035)t$ When you encounter simple interest problems, remember that simple interest is calculated using the formula: Interest = Principal × Rate × Time, or $I = Prt$ . Let's identify each component from the problem: the principal (P) is $1,200, the annual interest rate (r) is 3.5% = 0.035, and the time (t) is the variable we're solving for. Substituting these values into the formula gives us $I = 1200 × 0.035 × t$ , which can be written as $I = 1200(0.035)t$ . Looking at the answer choices: Choice A correctly applies the simple interest formula with all components in the right places. Choice B adds 0.035t to the principal amount, which would represent a balance calculation rather than interest earned, and incorrectly treats the rate as a dollar amount rather than a percentage. Choice C divides the principal by the rate and time, which has no basis in interest calculations and would actually decrease as time increases. Choice D adds the principal times time to the rate, mixing up the variables completely and treating the percentage rate as a standalone dollar amount. The key trap here is confusing interest earned with account balance. Remember that simple interest problems ask for either the interest earned (using $I = Prt$ ) or the total balance (Principal + Interest). Always convert percentages to decimals, and make sure you're answering what the question actually asks for—in this case, just the interest portion, not the total account value.
Jordan currently has twice as many baseball cards as Lee. If Lee has $x$ cards, and together they have 90 cards, which equation could be used to find $x$ ?
Answer: $x + 2x = 90$ When you encounter word problems involving relationships between quantities, start by identifying what each person has and translating the relationships into mathematical expressions. Here, Lee has $x$ cards, and Jordan has "twice as many" as Lee, which means Jordan has $2x$ cards. Since they have 90 cards total, you add Lee's cards plus Jordan's cards to equal 90. The correct equation is $x + 2x = 90$ (choice A). This represents Lee's $x$ cards plus Jordan's $2x$ cards equaling their combined total of 90 cards. You can verify this works: if Lee has 30 cards, Jordan has 60 cards, and $30 + 60 = 90$ . Choice B, $2x - x = 90$ , represents the difference between their card collections, not their total. This would mean Jordan has 90 more cards than Lee, which contradicts the given information. Choice C, $x \times 2 = 90$ , only accounts for Jordan's cards equaling 90, completely ignoring Lee's cards and the fact that 90 is their combined total. Choice D, $\dfrac{x}{2} + x = 90$ , suggests Jordan has half as many cards as Lee ( $\dfrac{x}{2}$ ), which is the opposite of what the problem states. Study tip: In relationship problems, always define what each variable represents, translate "twice as many" or similar phrases carefully, and make sure your equation matches what the problem is asking for (total, difference, individual amount, etc.).
A store marks up the wholesale price of an item by 35% to determine the retail price. If the wholesale price is $w$ dollars, which expression represents the retail price?
Answer: $1.35w$ When you encounter markup problems, you're dealing with percent increases. The key insight is that a markup means you pay the original price plus the additional percentage. To find the retail price when an item is marked up 35%, you need to calculate the wholesale price plus 35% of the wholesale price. This gives you $w + 0.35w$ . Since both terms contain $w$ , you can factor it out: $w(1 + 0.35) = 1.35w$ . This represents 100% of the original price plus the 35% markup. Choice A ( $1.35w$ ) is correct because it captures both the original wholesale price and the 35% markup in one clean expression. Choice B ( $0.35 + w$ ) incorrectly adds 35 cents rather than 35% of the wholesale price. This would only work if the markup were a flat fee, not a percentage. Choice C ( $35w$ ) represents a 3,500% markup (35 times the original price), which would be an astronomical increase that makes no business sense. Choice D ( $\frac{w}{1.35}$ ) gives you a price lower than the wholesale price, which represents a discount rather than a markup. This is backwards from what the problem describes. Remember this pattern: when something increases by a percentage, multiply the original amount by $(1 + \text{decimal form of percentage})$ . For increases, this multiplier is always greater than 1, which helps you quickly eliminate choices that would decrease the original value.
Maria is planning a fundraising dinner. She pays a flat fee of $85 to rent the hall plus $12 for each guest's meal. If Maria collected $g$ guests' ticket payments, which expression represents her total cost, in dollars, for the event?
Answer: $85 + 12g$ This question tests your ability to translate a word problem into a linear expression by identifying fixed costs versus variable costs. Maria has two types of expenses: a one-time hall rental fee of $85 (this stays the same regardless of how many guests attend) and a per-guest meal cost of $12 (this changes based on the number of guests). With $g$ guests, she pays $12 for each guest's meal, giving us $12g$ for the total meal costs. Her complete expenses are the fixed hall cost plus the variable meal costs: $85 + 12g$ . Let's examine why each answer choice is right or wrong: **A) $85 + 12g$ ** correctly separates the fixed cost ( $85) from the variable cost ($ $12g$ $). This matches our reasoning above. **B) $85g + 12$ ** incorrectly makes the hall rental fee variable by multiplying it by $g$ , suggesting Maria pays $85 per guest for the hall, which doesn't match the problem. **C) $(85 + 12)g$ ** treats both costs as per-guest expenses, meaning Maria would pay $97 per guest with no fixed costs. This ignores that the hall fee is a one-time charge. **D) $85 \div 12g$ ** uses division instead of addition, which makes no sense in this context since we're combining costs, not dividing them. Study tip: In cost problems, always identify what's fixed (stays the same) versus what's variable (changes with quantity). Fixed costs stand alone, while variable costs get multiplied by the quantity.
Carmen is purchasing $50 gift cards to give to each of her employees and also wants to buy one office coffee machine costing $280. If she spends a total of $1,080, which equation could be used to determine $e$ , the number of employees?
Answer: $50e + 280 = 1080$ When you encounter word problems asking you to write equations, your goal is to translate the written information into mathematical language by identifying what each part represents. Let's break down what Carmen is spending money on: $50 gift cards for each employee, plus one $280 coffee machine, totaling $1,080. The key insight is recognizing that if there are $e$ employees, and each gets a $50 gift card, then the total spent on gift cards is $50e$ (50 dollars times the number of employees). The correct equation is $50e + 280 = 1080$ (choice A). This represents: (cost per employee × number of employees) + (coffee machine cost) = (total spent). Let's examine why the other choices are wrong: Choice B ( $280e + 50 = 1080$ ) incorrectly suggests Carmen buys $e$ coffee machines at $280 each, plus something costing $50. This misinterprets what the variables represent. Choice C ( $50 + 280e = 1080$ ) implies Carmen spends only $50 total on gift cards regardless of employee count, then buys $e$ coffee machines. This contradicts the problem stating she buys one coffee machine. Choice D ( $50e - 280 = 1080$ ) subtracts the coffee machine cost instead of adding it, which doesn't make sense when calculating total expenses. Study tip: In word problems involving total costs, identify each expense category first, then determine whether each is fixed (like the single coffee machine) or variable (like gift cards that depend on employee count). Always add expenses when calculating totals.
The distance $d$ , in miles, that a car can travel depends on the number of gallons of fuel $g$ in its tank. The car averages 28 miles per gallon and already has enough fuel to travel 70 miles. Which equation models this relationship?
Answer: $d = 70 + 28g$ This is a linear relationship problem where you need to identify how two quantities change together. When you see questions about rates and starting amounts, think about what stays constant (the rate) and what changes (the input variable). The car gets 28 miles per gallon, so for every gallon $g$ you add, the car can travel an additional 28 miles. This gives you $28g$ miles from the fuel you're adding. But the car already has enough fuel to go 70 miles before you add anything. The total distance is the starting amount plus what you gain from additional fuel: $d = 70 + 28g$ . This matches choice A. Choice B ( $d = 28 + 70g$ ) incorrectly treats the 70 miles as the rate per gallon and the 28 miles as the starting amount. This reverses the given information. Choice C ( $d = 70 - 28g$ ) suggests that adding fuel decreases the distance, which makes no sense. This would mean the car loses 28 miles of range for each gallon added. Choice D ( $d = 70g - 28$ ) treats the existing 70 miles as a rate per gallon and subtracts the 28 miles per gallon, completely misinterpreting both pieces of information. Study tip: In linear relationship problems, identify the starting value (constant term) and the rate of change (coefficient of the variable). The formula structure is always: Total = Starting Amount + (Rate × Variable).
A recipe uses 3 cups of flour for every 5 cups of sugar. If a baker wants to use $s$ cups of sugar, which expression represents the number of cups of flour needed?
Answer: $\dfrac{3}{5}s$ This question tests your ability to set up proportional relationships and translate them into algebraic expressions. When you see a recipe or ratio problem, focus on identifying the constant relationship between the quantities. The recipe gives you a fixed ratio: 3 cups of flour for every 5 cups of sugar. This means that for any amount of sugar, the flour needed is always $\frac{3}{5}$ of that sugar amount. If you use $s$ cups of sugar, you multiply by this ratio: $\frac{3}{5}s$ cups of flour. You can verify this with the original ratio: when $s = 5$ , you get $\frac{3}{5} \times 5 = 3$ cups of flour, which matches the recipe perfectly. Looking at the wrong answers: Choice B gives you $\frac{5}{3}s$ , which flips the ratio and would give you more flour than sugar (when $s = 5$ , you'd get $\frac{25}{3} \approx 8.3$ cups of flour instead of 3). Choice C, $3 + 5s$ , incorrectly adds quantities instead of maintaining a proportional relationship—this would give you 28 cups of flour when using 5 cups of sugar. Choice D, $5 - 3s$ , subtracts and would actually give you negative flour amounts for most realistic values of $s$ . For ratio problems, always set up your multiplier as $\frac{\text{what you want}}{\text{what you're given}}$ . Here, you want flour and you're given sugar, so the multiplier is $\frac{\text{flour}}{\text{sugar}} = \frac{3}{5}$ .
Emily read a 300-page novel. She read $p$ pages on Monday and twice as many pages on Tuesday as on Monday. Which equation represents the number of pages Emily still has to read after Tuesday?
Answer: $300 - (p + 2p)$ When you encounter word problems involving multiple steps and unknown variables, break down what happens in sequence and translate each piece into mathematical expressions. Let's trace Emily's reading progress. She read $p$ pages on Monday. On Tuesday, she read "twice as many pages as on Monday," which means $2p$ pages. So her total pages read after Tuesday is $p + 2p = 3p$ pages. Since the novel has 300 pages total, the pages remaining equals the total pages minus the pages already read: $300 - (p + 2p)$ . This matches answer choice A. Now let's examine why the other options are incorrect. Choice B gives us $300 - (p - 2p) = 300 - (-p) = 300 + p$ . This expression would actually increase the number of pages remaining as $p$ increases, which makes no sense—reading more pages can't leave you with more pages to read. Choice C, $300 - 2p$ , only accounts for Tuesday's reading and completely ignores the $p$ pages read on Monday. This undercounts the total pages read. Choice D, $300p - 2$ , multiplies the total pages by the pages read on Monday, which has no logical connection to the problem's structure. Study tip: In multi-step word problems, always identify what each day or step contributes, add up all the parts, then apply the final operation. Write out "Monday: $p$ , Tuesday: $2p$ , Total read: $p + 2p$ " to avoid mixing up the relationships between different quantities.
Use the table above to write an equation for the total number of cupcakes, $T$ , sold during the week in terms of $d$ , the number sold on Friday.
Answer: $T = 235 + d$ Monday–Thursday sales sum to $40 + 52 + 63 + 80 = 235$ . Total cupcakes equal that constant plus Friday's sales $d$ : $T = 235 + d$ . B. Subtracts rather than adds. C. Multiplies, creating far too large a total. D. Divides, not a realistic aggregation method.
A delivery truck travels from warehouse A to warehouse B at 45 mph, then returns at 60 mph due to lighter traffic. If the total trip takes 3.5 hours, what equation represents this situation where d is the distance between warehouses?
Answer: $\frac{d}{45} + \frac{d}{60} = 3.5$ When you encounter distance, rate, and time problems involving round trips, remember the fundamental relationship: Time = Distance ÷ Rate. You need to set up equations for each leg of the journey and add the times together. For this problem, the truck travels distance d at 45 mph to warehouse B, taking $\frac{d}{45}$ hours. On the return trip, it travels the same distance d at 60 mph, taking $\frac{d}{60}$ hours. Since the total trip takes 3.5 hours, you add these times: $\frac{d}{45} + \frac{d}{60} = 3.5$ . Answer D correctly represents this situation by adding the time for each leg of the journey. Answer A is incorrect because $\frac{45 + 60}{d}$ puts the speeds in the numerator and distance in the denominator, which doesn't follow the Time = Distance ÷ Rate formula. This would give you an incorrect unit (speed per distance rather than time). Answer B is wrong because it subtracts the return time from the initial time ( $\frac{d}{45} - \frac{d}{60}$ ), which would give you the difference between travel times, not the total time. Answer C incorrectly multiplies distance by speed ( $45d + 60d$ ), which gives you distance squared rather than time. This completely misapplies the distance-rate-time relationship. Study tip: For round-trip problems, always identify each leg separately, write the time equation for each leg using Time = Distance ÷ Rate, then add or subtract the times based on what the problem asks for. Watch out for answer choices that flip the distance-rate relationship or use the wrong operation.
Javier bought 3 identical notebooks and 2 identical pens. A pen costs $p$ dollars and a notebook costs $n$ dollars. Which expression represents the total amount Javier spent, in dollars?
Answer: $3n + 2p$ When you encounter word problems involving multiple items with different costs, you need to carefully translate the language into mathematical expressions by identifying quantities and unit costs. Javier bought 3 notebooks at $n$ dollars each and 2 pens at $p$ dollars each. To find the total cost, you multiply each quantity by its unit price, then add: $(3 \times n) + (2 \times p) = 3n + 2p$ . This gives you the correct expression in choice A. Let's examine why the other options are incorrect. Choice B, $(3 + 2)(n + p)$ , represents buying 5 items where each item costs $(n + p)$ dollars. This would mean each notebook and pen costs the same amount, which contradicts the problem. Choice C, $3np + 2$ , incorrectly multiplies the number of notebooks by both unit prices, then adds 2 (not $2p$ ). This makes no mathematical sense in the context. Choice D, $n + p$ , only accounts for buying one notebook and one pen, completely ignoring the quantities specified. The key trap here is confusing addition with multiplication. Remember that when you buy multiple items, you multiply quantity times unit price for each type of item, then add those products together. Watch out for expressions that incorrectly combine quantities and prices, or that treat different items as having the same cost when they don't.
A taxi ride costs $3.50 for the first mile and $2.10 for each additional mile. If $d$ represents the total number of miles traveled (with $d > 1$ ), which expression gives the fare in dollars?
Answer: $3.50 + 2.10(d - 1)$ When you encounter word problems involving tiered pricing like taxi fares, you need to carefully identify the base cost versus the variable cost structure. This taxi charges $3.50 for the first mile, then $2.10 for each mile beyond that first one. Since $d$ represents total miles traveled, you need an expression that accounts for: (1) the fixed $3.50 first-mile charge, plus (2) the $2.10 charge applied only to the additional miles beyond the first. The correct approach is $3.50 + 2.10(d - 1)$ , which is choice A. The term $(d - 1)$ represents the additional miles after the first mile. For example, if you travel 4 miles total, you pay $3.50 for mile 1, then $2.10 for each of the remaining 3 miles: $3.50 + 2.10(3) = 9.80$ . Choice B ( $3.50d + 2.10$ ) incorrectly applies the first-mile rate to all miles, then adds a flat $2.10. Choice C ($ $2.10d + 3.50d$ $) charges both rates for every mile, which would be $5.60d$ total. Choice D ( $3.50 + 2.10d$ ) charges the base rate plus the additional rate for all miles, not just the extra ones. Study tip: In tiered pricing problems, identify what triggers each rate. Here, mile 1 triggers one rate, while miles 2, 3, 4... trigger another. Always subtract appropriately to isolate the quantity subject to each rate.
A smartphone plan charges a monthly base fee plus a charge per gigabyte of data used. Sarah's bill was $65 for using 4 GB, and Mike's bill was $89 for using 8 GB. What will be the cost for a customer who uses exactly 6 GB of data?
Answer: $77 Let b = base fee and r = rate per GB. Set up equations: b + 4r = 65 and b + 8r = 89. Subtracting: 4r = 24, so r = 6. Substituting: b + 4(6) = 65, so b = 41. For 6 GB: 41 + 6(6) = 41 + 36 = $77. Choice A ($74) results from using r = 5.5 (incorrect calculation). Choice C ($80) assumes the cost increases linearly between the two given points without solving for the actual rates. Choice D ($83) results from incorrectly calculating b = 47.
The perimeter of a rectangular garden is 88 meters. If the width is $w$ meters, the length is 10 meters more than twice the width. Which equation can be used to find $w$ ?
Answer: $2(w + (2w + 10)) = 88$ When you encounter a word problem about perimeter, you need to translate the given relationships into mathematical expressions, then apply the perimeter formula. Let's break down what we know: the width is $w$ meters, and the length is "10 meters more than twice the width." This means length = $2w + 10$ . Since perimeter of a rectangle equals 2(length + width), we get: $2(w + (2w + 10)) = 88$ . This matches answer choice A perfectly. The equation correctly represents the perimeter formula with our expressions for length and width substituted in. Now let's examine why the other choices are wrong: Choice B ( $w + 2w + 10 = 88$ ) only adds length and width once instead of using the perimeter formula that requires multiplying by 2. This would give you half the actual perimeter. Choice C ( $2w + 10 = 88$ ) sets just the length equal to the perimeter, completely ignoring the width. This is a common error when students confuse the length expression with the full perimeter equation. Choice D ( $4w + 10 = 88$ ) appears to come from incorrectly distributing: $2(w + (2w + 10)) = 2w + 4w + 20 = 6w + 20$ , not $4w + 10$ . This shows a calculation error in the distribution step. Study tip: Always write out what each variable represents before setting up your equation. For rectangle perimeter problems, remember the formula is $P = 2(\text{length} + \text{width})$ , and carefully translate any word relationships into algebraic expressions before substituting.
A contractor budgets $x$ dollars for materials and expects labor costs to be 1.8 times as much. Which expression represents the total budget, in dollars?
Answer: $x + 1.8x$ This question tests your ability to translate a word problem into an algebraic expression, specifically when one quantity is described as a multiple of another. When the problem states that labor costs are "1.8 times as much" as materials, this means labor costs equal $1.8x$ dollars (since materials cost $x$ dollars). To find the total budget, you add materials and labor costs together: $x + 1.8x = 2.8x$ dollars. Choice A ( $x + 1.8x$ ) correctly represents this relationship. It shows materials ( $x$ ) plus labor costs ( $1.8x$ ), which gives the complete budget. Choice B ( $1.8 + x$ ) incorrectly treats the 1.8 as a fixed dollar amount rather than a multiplier. This would mean labor costs are just $1.80 plus materials, which doesn't match the "1.8 times as much" relationship described. Choice C ( $\frac{x}{1.8}$ ) represents division, suggesting labor costs are a fraction of materials costs. This is backwards from what the problem states. Choice D ( $1.8x - x$ ) subtracts materials from labor costs, giving you the difference between the two amounts rather than the total budget. While this equals $0.8x$ , it doesn't answer what was asked. Study tip: When you see "times as much" in word problems, multiply the base amount by that factor. Always check whether the question asks for individual amounts or a total—here, "total budget" signals you need to add all costs together.

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