Need to find amount of a paycheck

Question

1/7 of pay was taken out of my check for taxes, 1/3 of the pay, after taxes was taken out on rent; 1/4 of the remaining amout was for phone and utilities, and 1/2 of the remaining amout was for groceries. She has $800 left. What was the original amount for?.

Answer 1

Hi Mike,

 

Let X = the original amount of pay

 

The amount left over at each step is one minus the fraction given. . . so if 1/7 of the pay is taken out in taxes, then 6/7 is left over.  We'll repeat this for each step. . .

 

6/7 x 2/3 x 3/4 x 1/2 = 36/168 which reduces to 3/14

 

She has $800 left over so X = 800 + 3X/14

 

X - 3X/14 = 800

 

Using 14 as a common denominator-->11X/14 = 800

 

Multiply each side by 14--> 11X = 11200

 

Divide both sides by 11--> X = 1018

 

Go through the steps of the problem to make sure this answer is correct.

 

Have fun.

 

Dan