Can't figure out how to solve this--how to set the problem up.

Question

Last Valentine’s Day, Ashley received not one but two boxes of chocolates! Ashley ate 3/5 of the chocolates in Box 1, and shared Box 2 with her brother, who ate 5/6 of that box. They ate the exact same number of chocolates. Which box had more chocolates?

Answer 1

So, we want to find out which box is bigger.

 

Let's call the first box of chocolates box A, and the second box of chocolates box B. 

 

Ashley ate 3/5 of box A, so we can say that Ashley ate 3/5 A chocolates. 

 

Her brother ate 5/6 of box B, so we can say that the brother ate 5/6 B chocolates. 

 

 

Now, the total number of chocolates that they ate were the same, so we know that:

 

3/5 A = 5/6 B.

 

 

Now, we can solve for either A or B. A is already on the left hand side, so let's solve for A. We multiply both sides of the above equation by 5/3 to get: 

 

A = 25/18 B. 

 

 

Now, which box is bigger? We know that 25/18 is greater than 1, so box A must be bigger! We can see this by observing that:

 

A = 25/18 B = (18/18 + 7/18) B = (1 + 7/18) B = B + 7/18 B. 

 

That is, A is as big as B plus 7/18 of B. 

 

 

Hope this helps!