ISEE Middle Level Quiz: Equation From A Situation
20 questions · exam conditions
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Equation From A SituationQuestion 1 of 20

Town A has a population of 12,000 and is growing by 250 people per year. Town B has a population of 15,000 and is decreasing by 150 people per year. Which equation can be used to find y, the number of years it will take for the two towns to have the same population?

12000 + 250y = 15000 - 150y
12000 + 250y = 15000 + 150y
250y - 150y = 15000 + 12000
12000 - 250y = 15000 + 150y
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ISEE Middle Level Quiz

ISEE Middle Level Quiz: Equation From A Situation

Practice Equation From A Situation in ISEE Middle Level with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Equation From A Situation, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Middle Level.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Town A has a population of 12,000 and is growing by 250 people per year. Town B has a population of 15,000 and is decreasing by 150 people per year. Which equation can be used to find y, the number of years it will take for the two towns to have the same population?

  1. 12000 + 250y = 15000 - 150y (correct answer)
  2. 12000 + 250y = 15000 + 150y
  3. 250y - 150y = 15000 + 12000
  4. 12000 - 250y = 15000 + 150y
Explanation: The population of Town A after y years will be its initial population plus the growth: 12000 + 250y. The population of Town B after y years will be its initial population minus the decrease: 15000 - 150y. To find when the populations are equal, we set these two expressions equal to each other: 12000 + 250y = 15000 - 150y.

Question 2

The temperature at 6:00 a.m. was -8°F. The temperature increased at a constant rate of 3°F per hour. Which equation can be used to find h, the number of hours it took for the temperature to reach 13°F?

  1. -8 + 3h = 13 (correct answer)
  2. -8 - 3h = 13
  3. 8 + 3h = 13
  4. 3h - 8 = 13
Explanation: The final temperature (13°F) is equal to the initial temperature (-8°F) plus the total increase. The total increase is the rate (3°F per hour) multiplied by the number of hours (h), which is 3h. So, the equation is -8 + 3h = 13.

Question 3

A train travels at 80 miles per hour for hh hours, going DD miles. Which equation is correct?

  1. D=80+hD=80+h
  2. h=80Dh=80D
  3. D=80hD=80h (correct answer)
  4. D=8hD=8h
Explanation: This question tests middle-level math skills: choosing an equation to model a situation. Understanding equations involves recognizing relationships between variables and constants as described in a scenario. In this example, the scenario describes a train traveling at 80 miles per hour for h hours, requiring an equation that shows distance equals rate times time (D = rt). Choice C is correct because D = 80h accurately models the relationship where distance equals the rate (80 mph) multiplied by time (h hours). Choice A incorrectly adds instead of multiplying, Choice B reverses the relationship making hours equal 80 times distance, and Choice D uses an incorrect rate of 8 instead of 80. To help students, reinforce the fundamental formula distance = rate × time and practice identifying which quantity is which in word problems. Common errors include confusing addition with multiplication in rate problems.

Question 4

Maya starts with 120120 dollars and saves 2525 dollars monthly for mm months, totaling TT. Choose the equation.

  1. T=120+25mT=120+25m (correct answer)
  2. T=25+120mT=25+120m
  3. T=120−25mT=120-25m
  4. T=120+25T=120+25
Explanation: This question tests middle-level math skills: choosing an equation to model a situation. Understanding equations involves recognizing relationships between variables and constants as described in a scenario. In this example, the scenario describes starting with $120 and adding $25 each month for m months, requiring an equation of the form T = initial amount + (monthly amount × months). Choice A is correct because T = 120 + 25m accurately models starting with $120 and adding $25 for each of m months. Choice B incorrectly reverses the constants, Choice C subtracts instead of adds, and Choice D doesn't include the variable m. To help students, emphasize identifying the starting value and the repeated action, then translating 'each month' or 'per month' into multiplication. Regular practice with savings and accumulation problems builds this skill.

Question 5

A cyclist rides at 18 miles per hour for tt hours. Which equation models distance dd?​​

  1. d=18+td=18+t
  2. d=18td=18t (correct answer)
  3. d=18td=\dfrac{18}{t}
  4. d=t−18d=t-18
Explanation: This question tests middle-level math skills: choosing an equation to model a situation. Understanding equations involves recognizing relationships between variables and constants as described in a scenario. In this example, the scenario describes a constant speed of 18 miles per hour multiplied by time t to find distance d, requiring an equation of the form d = speed × time. Choice B is correct because it accurately models the relationship using multiplication of the given speed and time variable. Choice C is incorrect because it divides instead of multiplies, a common error when students invert the rate relationship. To help students, teach identifying key parts of scenarios like velocity and time, and translating them into mathematical terms. Encourage practice with varied contexts such as cycling or driving to build flexibility in model creation.

Question 6

The sum of three consecutive odd integers is 141. If n represents the smallest of these integers, which equation models this situation?

  1. n + (n + 1) + (n + 2) = 141
  2. n + (n + 2) + (n + 4) = 141 (correct answer)
  3. 3n + 3 = 141
  4. n(n + 2)(n + 4) = 141
Explanation: If n is the smallest odd integer, the next consecutive odd integer is n + 2, and the one after that is n + 4. The sum of these three integers is n + (n + 2) + (n + 4). Setting this sum equal to 141 gives the equation n + (n + 2) + (n + 4) = 141.

Question 7

A salesperson earns a base salary of $400 per week plus an 8% commission on her total sales. Last week, her total earnings were $720. Which equation can be used to find S, her total sales in dollars for the week?

  1. 400 + 8S = 720
  2. 0.08(400 + S) = 720
  3. 400 + 0.08S = 720 (correct answer)
  4. 400S + 0.08 = 720
Explanation: The salesperson's total earnings are the sum of her base salary ($400) and her commission. The commission is 8% of her sales S, which is calculated as 0.08S. Therefore, the equation for her total earnings of $720 is 400 + 0.08S = 720.

Question 8

Planning a party at a community center costs $15 for a room rental plus $9.50 per person attending. If the total budget for the party is $186, which equation determines the number of people, p, that can attend?

  1. 15p + 9.50 = 186
  2. (15 + 9.50)p = 186
  3. 9.50(p + 15) = 186
  4. 15 + 9.50p = 186 (correct answer)
Explanation: The total cost is composed of a fixed cost (the $15 room rental) and a variable cost that depends on the number of people. The variable cost is $9.50 times the number of people, p, which is 9.50p. The total cost, which must equal the budget of $186, is the sum of these costs: 15 + 9.50p = 186.

Question 9

Maya's age is 5 years more than twice her brother's age. The sum of their ages is 32. Which equation can be used to find b, the brother's age?

  1. b + (2b - 5) = 32
  2. b + 2(b + 5) = 32
  3. 2b + 5 = 32
  4. b + (2b + 5) = 32 (correct answer)
Explanation: Let b be the brother's age. 'Twice her brother's age' is 2b. '5 years more than twice her brother's age' means Maya's age is 2b + 5. The sum of their ages is 32, which means the brother's age (b) plus Maya's age (2b + 5) equals 32. This gives the equation b + (2b + 5) = 32.

Question 10

A 500-gallon tank that started with 75 gallons of water is being filled at a rate of 40 gallons per minute. At the same time, water is draining out at a rate of 15 gallons per minute. Which equation determines the time, t, in minutes until the tank is full?

  1. 75 + (40 + 15)t = 500
  2. 75 + (40 - 15)t = 500 (correct answer)
  3. 40t - 15t = 500
  4. 75 + 40t = 500 - 15
Explanation: The net rate at which the tank is filling is the fill rate minus the drain rate: 40 - 15 = 25 gallons per minute. The amount of water added to the tank after t minutes is 25t. The total volume in the tank is the initial volume (75 gallons) plus the added volume (25t). To be full, this must equal 500 gallons. So, the equation is 75 + 25t = 500, which is equivalent to 75 + (40 - 15)t = 500.

Question 11

A jacket is on sale for 20% off its original price. An additional 5% sales tax is calculated on the discounted price. If the final price after the discount and tax is $84, which equation can be used to find the original price, p?

  1. 0.80p + 0.05p = 84
  2. p - 0.20p + 0.05 = 84
  3. 1.05(0.80p) = 84 (correct answer)
  4. 0.80(p + 0.05p) = 84
Explanation: The original price is p. A 20% discount means the price becomes p - 0.20p = 0.80p. The 5% sales tax is applied to this discounted price, so the total cost is the discounted price plus 5% of the discounted price: 0.80p + 0.05(0.80p). This can be factored as (1 + 0.05)(0.80p), which simplifies to 1.05(0.80p). The final price is $84, so 1.05(0.80p) = 84.

Question 12

A plumber charges a $75 service fee for a house call, plus $50 for each hour of work. Last week, the plumber earned a total of $275 for a single job. Which equation can be used to find h, the number of hours the plumber worked on that job?

  1. 75h + 50 = 275
  2. (75 + 50)h = 275
  3. 50h = 275
  4. 75 + 50h = 275 (correct answer)
Explanation: The plumber's total earning is the sum of the fixed service fee and the hourly charge. The service fee is $75. The hourly charge is $50 per hour for h hours, which amounts to 50h. The total earning of $275 is the sum of these parts, so the equation is 75 + 50h = 275.

Question 13

Jada has a collection of dimes and nickels worth a total of $4.15. She has 7 more dimes than nickels. Which equation can be used to find n, the number of nickels Jada has, if all values are expressed in cents?

  1. 5n + 10(n + 7) = 415 (correct answer)
  2. 5n + 10(n - 7) = 415
  3. 5(n + 7) + 10n = 415
  4. n + (n + 7) = 415
Explanation: Let n be the number of nickels. The number of dimes is n + 7. In cents, the value of the nickels is 5n and the value of the dimes is 10(n + 7). The total value is 415 cents. The equation is the sum of the values of the nickels and dimes: 5n + 10(n + 7) = 415.

Question 14

A recipe that makes 12 cookies requires 2 cups of flour. A baker wants to make 90 cookies and finds that he needs an additional 4 cups of flour. Which equation can be used to find c, the number of cups of flour the baker currently has?

  1. c - 4 = (90/12) * 2
  2. c + 4 = (12/90) * 2
  3. c + 4 = (90/12) * 2 (correct answer)
  4. c = (90/12) * 2 + 4
Explanation: First, determine the total amount of flour needed. The ratio of flour to cookies is 2 cups / 12 cookies. For 90 cookies, the total flour needed is (90/12) * 2. The amount of flour the baker has, c, plus the additional 4 cups he needs must equal this total amount. Therefore, the equation is c + 4 = (90/12) * 2.

Question 15

A mobile phone plan costs $45 per month, which includes 5 gigabytes of data. For each gigabyte of data used over the initial 5, the company charges an additional $8. Which equation represents the total monthly cost, C, for a month where a user consumes x gigabytes of data, assuming x is greater than 5?

  1. C = 45 + 8x
  2. C = 45 + 8(x - 5) (correct answer)
  3. C = 45 + 8(x + 5)
  4. C = 8x + 45(x - 5)
Explanation: The total cost C is the sum of the base fee ($45) and the cost for extra data. The number of extra gigabytes is the total gigabytes used, x, minus the 5 included gigabytes, which is (x - 5). The cost for this extra data is $8 per gigabyte, so the extra cost is 8(x - 5). Therefore, the total cost is C = 45 + 8(x - 5).

Question 16

In a basketball game, a player scored 31 points by making a combination of 2-point shots and 3-point shots. The player made 5 more 2-point shots than 3-point shots. If x represents the number of 3-point shots made, which equation models this situation?

  1. 2x + 3(x + 5) = 31
  2. 3x + 2(x + 5) = 31 (correct answer)
  3. 3x + 2(x - 5) = 31
  4. 5x + 5 = 31
Explanation: Let x be the number of 3-point shots. The number of 2-point shots is '5 more than' x, which is x + 5. The points from 3-pointers are 3x. The points from 2-pointers are 2(x + 5). The total points are the sum of these, which is 31. Therefore, the equation is 3x + 2(x + 5) = 31.

Question 17

A rectangular garden has a perimeter of 120 feet. The length of the garden is twice its width. Which equation represents the perimeter of the garden in terms of its width, w?

  1. w(2w) = 120
  2. w + 2w = 120
  3. 2w + 2(2w) = 120 (correct answer)
  4. 2(w + 2w) = 60
Explanation: Let the width be w. The length is twice the width, so L = 2w. The formula for the perimeter of a rectangle is P = 2L + 2w. Substituting L = 2w and P = 120 into the formula gives 120 = 2(2w) + 2w. This can also be written as 2w + 2(2w) = 120.

Question 18

The measure of an angle is 18 degrees more than one-third the measure of its supplementary angle. If x is the measure of the angle, which equation correctly represents this relationship?

  1. x = (1/3)(90 - x) + 18
  2. x + (1/3)x + 18 = 180
  3. x = 3(180 - x) + 18
  4. x = (1/3)(180 - x) + 18 (correct answer)
Explanation: Let the angle be x. Its supplement is 180 - x. 'One-third the measure of its supplement' is (1/3)(180 - x). '18 degrees more than' this quantity is (1/3)(180 - x) + 18. Since this is equal to the measure of the angle x, the equation is x = (1/3)(180 - x) + 18.

Question 19

A store has 150150 dollars fixed costs and makes 99 dollars profit per product sold. For pp products, which equation models RR?

  1. R=150p+9R=150p+9
  2. R=150+9pR=150+9p (correct answer)
  3. R=150−9pR=150-9p
  4. R=9pR=9p
Explanation: This question tests middle-level math skills: choosing an equation to model a situation. Understanding equations involves recognizing relationships between variables and constants as described in a scenario. In this example, the scenario describes a store with $150 fixed costs that makes $9 profit per product, requiring an equation of the form R = fixed costs + (profit per product × products). Choice B is correct because R = 150 + 9p accurately models starting with $150 in fixed costs and adding $9 profit for each of p products sold. Choice A incorrectly reverses the coefficients making it 150p + 9, Choice C subtracts the profit instead of adding it, and Choice D omits the fixed costs entirely. To help students, teach them to identify fixed versus variable components and understand that profits typically add to totals. Business contexts like this help students see real-world applications of linear equations.

Question 20

A lab uses 88 grams of Chemical A plus 33 grams per trial of Chemical B. For tt trials, write GG.

  1. G=8+3tG=8+3t (correct answer)
  2. G=(8+3)tG=(8+3)t
  3. G=8−3tG=8-3t
  4. G=3+8tG=3+8t
Explanation: This question tests middle-level math skills: choosing an equation to model a situation. Understanding equations involves recognizing relationships between variables and constants as described in a scenario. In this example, the scenario describes using 8 grams of Chemical A (fixed amount) plus 3 grams per trial of Chemical B, requiring an equation of the form G = fixed amount + (amount per trial × trials). Choice A is correct because G = 8 + 3t accurately models using 8 grams initially plus 3 grams for each of t trials. Choice B incorrectly groups the constants before multiplying, Choice C subtracts instead of adds, and Choice D reverses the coefficients. To help students, teach them to distinguish between fixed amounts (used once) and variable amounts (used repeatedly). Practice identifying keywords like 'per trial' or 'each time' that signal multiplication.