Question

There were 25 doughnuts in the box. Jim had ( 2)/(3) as many doughmuts as Ben. If Jim and Ben together finished ( 4)/(5) of the doughnuts in the box, how many doughnuts did Jim eat?

Answer 1

To determine how many doughnuts Jim ate, we set up two equations representing the relationship between the doughnuts Jim and Ben ate and the fractions given. By solving these simultaneously, we find out that Jim ate 8 doughnuts.

Step-by-step explanation:

The question is asking how many doughnuts Jim ate if Jim had (2/3) as many doughnuts as Ben and together they ate (4/5) of the doughnuts in the box, with a total of 25 doughnuts in the box.

Let's denote Ben's number of doughnuts as B and Jim's as J. Since Jim had (2/3) as many doughnuts as Ben, we have J = (2/3)B. Together, they ate (4/5) of the entire box, so J + B = (4/5) × 25 doughnuts.

We can set up the equations as follows:

1. B + J = (4/5) × 25
2. J = (2/3)B

Now, we solve these equations to find the number of doughnuts J that Jim ate.

First, we substitute J from the second equation into the first equation:

B + (2/3)B = 20
(5/3)B = 20
B = (3/5) × 20
B = 12

Now we can find J:

J = (2/3) × 12 = 8

Therefore, Jim ate 8 doughnuts.