Algebra word Problem

Question

Ali and Keesha found a sale in a sporting goods store. Ali spend $33 on 2 pairs of shorts and 3 packages of socks. Keesha spent $27 on 1 pair of shorts and 5 packages of socks. How much does each item cost?

Answer 1

Let x = price of shorts

Let y = price of socks

 

now create the equations

 

2x + 3y = 33   (2 shorts + 3 socks equal 33)

1x + 5y = 27   (1 shorts + 5 socks equal 27)

 

multiply the second equation by 2 and subtract

 

2x + 3y =33

2x +10y =54  (multiplied by 2)

 

now subtract

 

-7y = -21

 

y = 3

 

now solve for x

 

2x + 3(3) = 33

2x + 9 = 33

2x =24

x = 12

 

so shorts cost $12

and socks cost $3