Question

Last year, a baseball team purchased new equipment. Ray, the equipment manager, paid $20 per bat and $12 per glove, spending a total of $552. Ray bought a total of 34 pieces of equipment.

a) Number of bats bought: _____, Number of gloves bought: _____
b) Number of bats bought: 18, Number of gloves bought: 16
c) Number of bats bought: 16, Number of gloves bought: 18
d) Number of bats bought: 20, Number of gloves bought: 14

Answer 1

After solving the simultaneous equations based on the cost of the bats and gloves and the total number of items purchased, we determined that Ray, the equipment manager, bought 18 bats and 16 gloves with the $552 he had available.

Step-by-step explanation:

Last year, a baseball team purchased new equipment. Ray, the equipment manager, needed to allocate a budget wisely to purchase a combination of bats and gloves to benefit the team. Through a mathematical approach, we can determine the quantity of each item Ray bought. He had a total of $552 to spend with bats costing $20 each and gloves costing $12 each. The problem also tells us Ray bought a total of 34 pieces of equipment.

Let's define the variables:

• Let b be the number of bats.
• Let g be the number of gloves.

Based on the given information, we can set up the following equations to represent the situation:

1. 20b + 12g = 552 (Total amount spent)
2. b + g = 34 (Total pieces of equipment)

Solving these equations simultaneously, we can find the exact number of bats and gloves purchased.

From the second equation, we can express g in terms of b:

g = 34 - b

Substituting this into the first equation:

20b + 12(34 - b) = 552
20b + 408 - 12b = 552
8b = 144
b = 18

Thus, Ray bought 18 bats. Now we can calculate the number of gloves:

g = 34 - b
g = 34 - 18
g = 16

Therefore, the correct answer is:

b) Number of bats bought: 18, Number of gloves bought: 16