Question

The coach of an intramural baseball club needs to order baseballs and bats. He visits a local sporting goods store and notices that one bucket of baseballs and one bat costs a total of $50. The coach decides to order 3 buckets of baseballs and 5 bats for a total cost of $220.

However, due to a change in the number of expected participants in the intramural baseball club, the coach decides to change the order. Which of the following orders could the coach make and have the same cost per bucket of baseballs and the same cost per bat as in the original order? Select ALL that apply.

2 buckets of baseballs and 4 bats for a total cost of $170


3 buckets of baseballs and 6 bats for a total cost of $270


4 buckets of baseballs and 4 bats for a total cost of $220


5 buckets of baseballs and 7 bats for a total cost of $320


6 buckets of baseballs and 8 bats for a total cost of $440

Answer 1

Let b = cost per bucket and t = cost per bat.
From b + t = 50 and 3b + 5t = 220:
3b + 5(50 − b) = 220 → 3b + 250 − 5b = 220 → −2b = −30 → b = 15, t = 35.

Compute totals:
- 2b + 4t = 2(15) + 4(35) = 30 + 140 = 170 ✔
- 3b + 6t = 45 + 210 = 255 ✖
- 4b + 4t = 60 + 140 = 200 ✖
- 5b + 7t = 75 + 245 = 320 ✔
- 6b + 8t = 90 + 280 = 370 ✖

So the orders that could have the same unit prices are:
- 2 buckets and 4 bats for $170
- 5 buckets and 7 bats for $320