at first, prairie had 10%....

Question

Simple pictures may help you solve this problem.

 

At first, Prarie had 10% more than the cost of a computer game. After Prarie spent $7.50, she had 15% less than the cost of the computer game. How much did the computer game cost? How much money did Prarie have at first? Explain your reasoning. 

Answer 1

Cost of computer game = $x

Prarie has $y at first

 

At first, Prarie had 10% more than the cost of a computer game

 

y=x +10%x 

 y =x+0.1x  

y=1.1 x        equation 1

 

 

After Prarie spent $7.50, 

 

She has =y-7.50  which is 15% less than the cost of the computer game

 

y-7.50 = x - 15% of x

y-7.5  =x-0.15x

y= x-0.15x+7.5

y=0.85x +7.5    equation 2

 

from equation 1 and 2

 

1.1x = 0.85x +7.5

 

0.15x =7.5

 

x = 50

 

substitute x=50 in eq 1

y=1.1x

y=1.1(50)

y= 55

 

Cost of computer game = $x = $50
Prarie has $y at first=$55