Arithmetic Word Problems Flashcards

Machine A can produce 20 widgets per hour, and Machine B can produce 30 widgets per hour. Working together at their respective rates, how many hours will it take for them to produce a total of 250 widgets?

Answer: 5 hours

To solve this, first find the combined production rate of both machines. Machine A produces 20 widgets/hour and Machine B produces 30 widgets/hour, so their combined rate is 20 + 30 = 50 widgets per hour. Then, divide the total number of widgets needed (250) by the combined hourly rate (50): 250 / 50 = 5 hours.

An electronics store advertises a laptop for $150. A customer uses a coupon for a 20% discount, and then an 8% sales tax is calculated on the discounted price. What is the final cost for the customer?

Answer: $129.60

First, calculate the discount: 20% of $150 is $30. The discounted price is $150 - $30 = $120. Next, calculate the sales tax on this discounted price: 8% of $120 is $9.60. Finally, add the sales tax to the discounted price to get the final cost: $120 + $9.60 = $129.60.

A student has scores of 85, 92, 78, and 88 on four exams. What score must the student achieve on the fifth and final exam to have an average score of exactly 87 across all five exams?

Answer: 92

To achieve an average of 87 over five exams, the total sum of the scores must be 87 * 5 = 435. The sum of the first four scores is 85 + 92 + 78 + 88 = 343. To find the required score on the fifth exam, subtract the current sum from the required total sum: 435 - 343 = 92.

A recipe for a fruit punch calls for a ratio of 3 parts cranberry juice to 2 parts ginger ale. If a party host needs to make a large batch and uses 8 cups of ginger ale, how many cups of cranberry juice are required?

Answer: 12 cups

The problem can be solved by setting up a proportion: (3 cups cranberry / 2 cups ginger ale) = (x cups cranberry / 8 cups ginger ale). To solve for x, you can cross-multiply (3 * 8 = 2 * x) which gives 24 = 2x, so x = 12. Alternatively, you can see that the amount of ginger ale (8 cups) is 4 times the amount in the ratio (2 cups), so you must multiply the cranberry juice amount by 4 as well: 3 * 4 = 12 cups.

A retailer buys 500 units of a product at a cost of $12 each. The shipping cost for the entire order is $1,000. If all 500 units are sold for $25 each, what is the retailer's total gross profit?

Answer: $5,500

First, calculate the total revenue: 500 units * $25/unit = $12,500. Next, calculate the total costs. The cost of goods is 500 units * $12/unit = $6,000. The total cost is the cost of goods plus shipping: $6,000 + $1,000 = $7,000. Finally, calculate the gross profit by subtracting total costs from total revenue: $12,500 - $7,000 = $5,500.

A cyclist travels to a destination 120 miles away at a constant speed of 60 mph. He returns along the same route at a constant speed of 40 mph. What is the average speed for the entire round trip?

Answer: 48 mph

Average speed is Total Distance / Total Time. First, calculate the time for each leg of the journey. Time to destination = 120 miles / 60 mph = 2 hours. Time to return = 120 miles / 40 mph = 3 hours. The total distance is 120 + 120 = 240 miles. The total time is 2 + 3 = 5 hours. Average speed = 240 miles / 5 hours = 48 mph. Simply averaging the two speeds (60+40)/2 = 50 is incorrect.