A sports apparel supplier offers teams the option of purchasing extra apparel for players. A volleyball team purchases 15 jackets and 12 pairs of sweatpants for $348. A basketball team purchases 8 jackets and 8 pairs of sweatpants for $200. Let x represent the price of a jacket and let y represent the price of a pair of sweatpants. Which system of equations can be used to find the price of each item?

Question

Yggdrasil · Answer

x = jacket price
y = sweatpants price

(1) 15x + 12y = 348
(2) 8x + 8y = 200

Equations are too confusing so use elimination method
we need a common coefficient between equations
we multiply (1) by 2
we multiply (2) by -3
to get 24y and -24y

our new equations are 
(1) 30x + 24y = 696
(2) -24x + -24y = -600

We add them together
30x + 24y - 24y - 24x = 696 - 600
30x - 24x = 96
6x = 96
divide both sides by 6
x = 16
we know the price of a jacket, now to find the price of sweatpants. 
substitute x = 16 into one of the equations
15(16) + 12y = 348
240 + 12y = 348
12y = 108
divide both sides by 12
y = 9

price of jacket = $16
price of sweatpants = $9

Tranquility · Answer

Do note that the question asks what system of equation can be used to find the solution. It doesn't ask us to solve the system of equations