Last year, a baseball team paid $20 per bat and $12 per glove, spending a total of $1040. this year, the prices went up to $25 per bat and $16 per glove. the team spent $1350 to purchase the same amount of eqipment as last year. how many bats and gloves did the team purchase each year?

Hey there!

You can solve this question using a system of equations. Let x be the number of bats and y be the number of gloves. The first equation will contain 20x and 12y and the second equation will contain 25x and 16y. The equations will be set to the total amount of money they were given per year:

20x + 12y = 1040
25x + 16y = 1350

To solve the system, make one of the terms the same but have the opposite signs using multiplication. This will cancel one of them out. It can be any term you see is easiest. Just make sure that one of the terms is set to 0 by the end of this step. 

–1.25(20x + 12y = 1040)
25x + 16y = 1350

In this case, you can multiply the first equation by –1.25 to make 20x into –25x. This will cancel out the x term. Make sure you multiply the entire first equation. 

–25x + (–15y) = –1300
25x + 16y = 1350

Now, just add the two equations together. 

0x + 1y = 50
y = 50

Now that you know what y is equal to, plug it into your first equation (the original) to find x. This pair will be your answer. 

20x + 12y = 1040
20x + 12(50) = 1040
20x + 600 = 1040
20x = 440
x = 22

So, the pair is (22, 50). This means that the team bought 22 bats and 50 gloves. 

Hope this helped you out! :-)