- A clothing store is having a sale where all items are marked down 35% from the original price, and then an additional $12.50 is deducted at checkout. If a jacket's final price after both discounts is $67.25, what was the original price?
Answer: $122.69
Work backwards from the final price. Before the $12.50 deduction: $67.25 + $12.50 = $79.75. This $79.75 represents 65% of the original price (since 35% was marked down). Set up equation: 0.65x = $79.75. Solve: x = $79.75 ÷ 0.65 = $122.69. Choice B ($132.69) might result from using 0.75 instead of 0.65. Choice C ($112.69) might result from calculation errors. Choice D ($142.69) might result from using 0.55 instead of 0.65.
- A recipe calls for 2.75 cups of flour, but you want to make 0.6 of the original recipe. If flour costs $0.89 per cup, how much will the flour for your adjusted recipe cost?
Answer: $1.47
First, calculate the amount of flour needed: 2.75 × 0.6 = 1.65 cups. Then calculate the cost: 1.65 × $0.89 = $1.4685, which rounds to $1.47. Choice B ($1.57) might result from incorrectly calculating 2.75 × 0.6 as 1.75 cups. Choice C ($1.37) might result from calculation errors. Choice D ($1.67) might result from adding instead of multiplying one of the steps.
- A customer buys 3 notebooks at $2.25 each and a pen for $1.50. If the customer pays with a $10 bill, how much change should they receive?
Answer: $1.75
First, calculate the total cost of the notebooks: 3 × $2.25 = $6.75. Next, add the cost of the pen to find the total purchase price: $6.75 + $1.50 = $8.25. Finally, subtract the total cost from the payment to find the change: $10.00 - $8.25 = $1.75.
- What is the product of 0.25 and 0.08?
Answer: 0.02
To multiply 0.25 by 0.08, first multiply the numbers without decimals: 25 × 8 = 200. Then, count the total number of decimal places in the original numbers (two in 0.25 and two in 0.08, for a total of four). Place the decimal point four places from the right in the product: 0.0200, which simplifies to 0.02.
- A baker mixes 3.5 pounds of flour that costs $0.80 per pound with 1.5 pounds of sugar that costs $1.20 per pound. What is the total cost of these ingredients?
Answer: $4.60
First, calculate the cost of the flour: 3.5 pounds × $0.80/pound = $2.80. Next, calculate the cost of the sugar: 1.5 pounds × $1.20/pound = $1.80. Finally, add the two costs together to find the total cost: $2.80 + $1.80 = $4.60.
- A roll of fabric contains 25 meters. A piece measuring 8.75 meters is cut from it, and then another piece measuring 5.5 meters is cut. How much fabric is left on the roll?
Answer: 10.75 meters
First, find the total amount of fabric that was cut by adding the two lengths: 8.75 + 5.5 = 14.25 meters. Then, subtract the total cut amount from the original length of the roll: 25 - 14.25 = 10.75 meters.
- A family buys 4 adult movie tickets for $12.25 each and 2 child tickets for $8.50 each. How much more did the family spend on adult tickets than on child tickets?
Answer: $32.00
First, calculate the total cost of the adult tickets: 4 × $12.25 = $49.00. Next, calculate the total cost of the child tickets: 2 × $8.50 = $17.00. Finally, find the difference between the two costs: $49.00 - $17.00 = $32.00.
- A 1.5-liter bottle of juice costs $3.60. A 2.5-liter bottle of the same juice costs $5.50. What is the difference in the cost per liter between the two bottles?
Answer: $0.20
First, find the cost per liter for each bottle. For the smaller bottle: $3.60 ÷ 1.5 liters = $2.40 per liter. For the larger bottle: $5.50 ÷ 2.5 liters = $2.20 per liter. Then, find the difference between the two unit costs: $2.40 - $2.20 = $0.20.
- A rectangular garden has a length of 5.4 meters and a width of 3.5 meters. What is the area of the garden in square meters?
Answer: 18.9
The area of a rectangle is calculated by multiplying its length by its width. Area = 5.4 meters × 3.5 meters = 18.9 square meters.
- The total weight of three packages is 15.2 kilograms. If the first package weighs 4.75 kilograms and the second weighs 6.5 kilograms, what is the weight of the third package?
Answer: 3.95 kg
First, add the weights of the two known packages: 4.75 + 6.5 = 11.25 kg. Then, subtract this sum from the total weight to find the weight of the third package: 15.2 - 11.25 = 3.95 kg.
- A package of 8 batteries costs $9.92. At this same rate, what would be the cost of 5 batteries?
Answer: $6.20
First, find the cost of a single battery (the unit price) by dividing the total cost by the number of batteries: $9.92 ÷ 8 = $1.24 per battery. Then, multiply the unit price by the desired number of batteries: $1.24 × 5 = $6.20.
- The price of a shirt is $24.50. The sales tax is 6% (or 0.06). What is the total cost of the shirt, including tax?
Answer: $25.97
First, calculate the amount of sales tax by multiplying the price by the tax rate: $24.50 × 0.06 = $1.47. Then, add the tax to the original price to find the total cost: $24.50 + $1.47 = $25.97.
- A metal rod is 5 meters long. A piece of 1.875 meters is cut off. What is the length of the remaining piece?
Answer: 3.125 meters
To find the length of the remaining piece, subtract the length of the cut piece from the original length of the rod. It is helpful to write 5 as 5.000 to align the decimal places: 5.000 - 1.875 = 3.125 meters.
- Mark starts the month with $250.50 in his account. He spends $85.25 on groceries and pays two bills of $45.75 each. How much money is left in his account?
Answer: $73.75
First, calculate the total cost of the two bills: 2 × $45.75 = $91.50. Next, calculate total spending by adding the groceries: $85.25 + $91.50 = $176.75. Finally, subtract the total spending from the starting balance: $250.50 - $176.75 = $73.75.
- A swimming pool is being filled at a rate of 45.8 gallons per minute. At the same time, water is being drained at a rate of 12.3 gallons per minute for cleaning purposes. If the pool currently contains 1,247.5 gallons and needs to reach 2,850.0 gallons, how long will it take to fill?
Answer: 47.8 minutes
Net filling rate: 45.8 - 12.3 = 33.5 gallons per minute. Amount needed: 2,850.0 - 1,247.5 = 1,602.5 gallons. Time required: 1,602.5 ÷ 33.5 = 47.84 minutes, which rounds to 47.8 minutes. Choice B (48.2) might result from calculation errors. Choice C (47.4) might result from rounding errors. Choice D (48.6) might result from using the wrong net rate.
- What is the value of the expression 12.5−2×4.25?
Answer: 4.0
According to the order of operations, multiplication should be performed before subtraction. First, calculate the product: 2 × 4.25 = 8.5. Then, perform the subtraction: 12.5 - 8.5 = 4.0.
- A runner's times for four laps were 55.2 seconds, 56.1 seconds, 54.9 seconds, and 55.4 seconds. What was the average lap time in seconds?
Answer: 55.4
To find the average, first sum the four lap times: 55.2 + 56.1 + 54.9 + 55.4 = 221.6 seconds. Then, divide the total time by the number of laps: 221.6 ÷ 4 = 55.4 seconds.
- An employee earns $14.50 per hour and works 38.5 hours in one week. What are the employee's total gross earnings for the week?
Answer: $558.25
To find the total gross earnings, multiply the hourly wage by the number of hours worked: $14.50 × 38.5 = $558.25.
- A developer wants to divide a 14.5-acre plot of land into 6 equal-sized lots. What is the acreage of each lot, rounded to the nearest tenth of an acre?
Answer: 2.4 acres
To find the size of each lot, divide the total acreage by the number of lots: 14.5 ÷ 6 ≈ 2.4166... acres. To round to the nearest tenth, look at the hundredths digit (1). Since it is less than 5, round down to 2.4 acres.
- A piece of wood is 6.5 feet long. If 1 foot is approximately 0.305 meters, what is the length of the wood in meters, rounded to the nearest hundredth?
Answer: 1.98
To convert the length from feet to meters, multiply the length in feet by the conversion factor: 6.5 × 0.305 = 1.9825 meters. The question asks to round to the nearest hundredth. Since the digit in the thousandths place is 2, we round down. The length is approximately 1.98 meters.
