word problem

Question

Ellen uses 2/7 of her money to buy a book. She uses 2/5 of the remaining money to buy a bag. Ellen has $15 left. How much money did she have at first?

Answer 1

Cost of Book = Total Money * 2/7

Cost of Bag = Total Money * 5/7 * 2/5

or

Cost of Bag = Total Money * 10/35 or Total Money * 2/7

 

since she used 2/5 of a portion of the remaining money (1-(2/7)=5/7)

 

Total Money (T) = Cost of Book + Cost of Bag + $15

 

Cost of both Book and Bag = T(2/7) + T(2/7) or T(4/7)

 

T = T(4/7) + $15

 

Divide by T

 

1 = 4/7 + (15/T)

 

Subtract by 4/7

 

1 - (4/7) = 15/T

 

3/7 = 15/T

 

Multiply by T

 

3T/7 = 15

 

Multiply by 7

 

3T = 105

 

Divide by 3

 

T = 35.

 

So, Ellen had $35.

 

Let check the answer.

 

Cost of Book = $35 * 2/7 = $10

Remaining Money = $35 - $10 ... $25

 

Cost of Bag = $25 * 2/5 = $10

 

Remain Money = $25 - $10 = $15

 

Cheers!

 

 

 

Answer 2

In this problem you have to work backwards. So since she used 2/5 of a portion of the remaining money, a number variable x(2/5)=15. So you try to figure out what x is. 

 

x(2/5)=15 --------------> 2x=75 ---------------> x = 37.5.

               Multiply by 5               Divide by 2

Then you do the same for the beginning portion being 2/7 portion ending to be 37.5.

 

y(2/7)=37.5 -------------> 2y=262.5 -------------> y =131.25

                  Multiply by 7                Divide by 2

 

I would just double check myself at this point just to be sure.

 

So, 131.25(2/7) = 37.5 Then 37.5(2/5) = 15. So since it ended with 15, 131.25 is your answer.