Matt spent2/5 of his money on food and 1/3 of the remainder on a book and remained with 60.00.

Question

How much did she have first?

Answer 1

Matt spent 2/5 of his money.  After that he had 3/5 of it remaining.

 

Out of that 3/5, he spent a 1/3 of the 3/5 on a book.  The word "of" tells us to multiply the two fractions, and

1/3  x  3/5 = 1/5.  So he spent 1/5 of the his money on the book.

 

So far, Matt has spent 2/5 + 1/5 = 3/5 of his money.

 

Since he has spent 3/5 of his money, Matt has 2/5 of his money remaining.

 

If m = the amount of money he had at first,  Matt has 2/5 m remaining.

 

Since Matt has $60 remaining, 2/5 m = 60

 

To solve for m, we divide both sides of the equation by 2/5.

 

So m = 60/ 2/5 =  150.  So, Matt started with $150.