Question

9. The basketball team sold t-shirts and hats at a fundraiser. They sold a total of 23 items and made a

profit of $154. They made a profit of $8 from each t-shirt sold and a profit of $10 from each hat sold.
Identify your variables. Then, write and solve a system of equations to find the number of t-shirts and
hats the basketball team sold.

Answer 1

t-shirts = 8, hats= 15

Explanation:

let the no of of t-shirt be x

and the no of hats be y

`x+y= 23-----------1`

`8x+10y= 154---------2`

solving equations 1 and 2 simultaneously we have

multiplying equation 1 by 8 and subtracting from 2 we have

`8x+8y=184-------------4\\-8x+10y=154------------2`

`=0x-2y=30`

`y=(-30)/(2) \\y=-15`

y= 15

substituting y= 15 in equation 1 to find x we have

`x+15=23\\x=23-15\\x= 8`

x=8