How mich did each persons spend?

Question

At shopping A used 1/4 of her money, B 1/5 of her money and C 1/2 of her money, they all had the same amount. A used 10$ more then B. How much money did each of them have before shopping?

 

 

Answer 1

A, B, and C "all had the same amount."  This is very important in this problem.  The problem asks us to determine it: "How much money did each of them have before shopping?"    Let this amount be x.

 

A used  (1/4)x

B used  (1/5)x

C used  (1/2)x

 

So far, no information helps determine x.  We need more.

 

"A used 10$ more then B"      means    

(1/4)x = $10 + (1/5)x                       (read this along with above)

 

Solve for x:

     5x = 200 + 4x             (multiply by 20 to get rid of fractions)

      x  = 200                (subtract 4x from both sides)

 They each started with $200.

 

Checking (very important):

A spent (1/4)(200) = 50

B spent (1/5)(200  = 40

  Is 50 = 10 + 40    ?

      50  =  50   ? yes