Unit Rates - Pre Algebra
- A recipe calls for 3 cups of flour to make 18 muffins. Sarah wants to make 42 muffins but only has 6.5 cups of flour available. Based on the recipe's unit rate, how much additional flour does she need? Answer: cups Unit rate: 3 cups ÷ 18 muffins = 1/6 cup per muffin. For 42 muffins: 42 × (1/6) = 7 cups needed. Sarah has 6.5 cups. Additional flour needed: 7 - 6.5 = 0.5 cups. Choice A is correct. Choice B represents a calculation error. Choice C might result from incorrect unit rate calculation. Choice D gives the total needed, not the additional amount.
- A streaming service charges different rates in three countries. In Country A, the monthly subscription costs $12.99 and includes 2 premium channels. In Country B, the cost is $18.50 for 4 premium channels. In Country C, the cost is $23.75 for 5 premium channels. Which country offers the best rate per premium channel, and what is that rate? Answer: Country B at $4.63 per channel Country A: $12.99 ÷ 2 = $6.495 per channel. Country B: $18.50 ÷ 4 = $4.625 per channel. Country C: $23.75 ÷ 5 = $4.75 per channel. Country B offers the best rate at approximately $4.63 per channel. Choice B is correct. Choice A gives Country A's rate, which is the highest. Choice C gives Country C's rate and amount correctly but it's not the best rate. Choice D has the wrong rate for Country B.
- At a printing company, Machine X prints 240 pages in 8 minutes, while Machine Y prints 180 pages in 5 minutes. If both machines run simultaneously for 20 minutes, how many more pages will the faster machine print compared to the slower machine? Answer: pages Machine X rate: 240 pages ÷ 8 minutes = 30 pages/minute. Machine Y rate: 180 pages ÷ 5 minutes = 36 pages/minute. Machine Y is faster. In 20 minutes: Machine Y prints 36 × 20 = 720 pages, Machine X prints 30 × 20 = 600 pages. Difference: 720 - 600 = 120 pages. Choice A is correct. Other choices represent various calculation errors or using wrong time periods.
- A cyclist travels 24 miles in the first hour, then 18 miles in the second hour due to headwinds. In the third hour, with favorable winds, she travels 30 miles. What was her average speed for the portion of the trip where she traveled faster than 20 miles per hour? Answer: miles per hour First hour: 24 mph (faster than 20). Second hour: 18 mph (not faster than 20). Third hour: 30 mph (faster than 20). For the portions faster than 20 mph: total distance = 24 + 30 = 54 miles, total time = 1 + 1 = 2 hours. Average speed = 54 ÷ 2 = 27 mph. Choice B is correct. Choice A represents a calculation error. Choice C gives only the third hour's speed. Choice D gives the total distance for the qualifying portions but not the rate.