Question

At a eating contest, Andy ate 5 more than Barry, while Carl ate 10 less than Barry. If the three ate a total of 103 hot dogs, how many did each eat?

Answer 1

Answer:Andy ate 41 hot dogs.

Barry ate 36 hot dogs.

Carl ate 26 hot dogs.

Explanation:

Let x represent the number of hot dogs that Andy ate at the eating contest.

Let y represent the number of hot dogs that Barry ate at the eating contest.

Let z represent the number of hot dogs that Carl ate at the eating contest.

At the eating contest, Andy ate 5 more than Barry, this means that

x = y + 5

Carl ate 10 less than Barry. This means that

z = y - 10

If the three ate a total of 103 hot dogs, it means that

x + y + z = 103 - - - - - - - - -1

Substituting x = y + 5 and z = y - 5 into equation 1, it becomes

y + 5 + y + y - 10 = 103

3y = 103 + 10 - 5 = 108

y = 108/3 = 36

x = y + 5 = x = 36 + 5 = 41

z = y - 10 = z = 36 - 10 = 26

Answer 2

Barry ate 36 hot dogs.

Andy at 36+5 = 41 hot dogs.

Carl ate 36-10 = 26 hot dogs.

Explanation:

This question can be solved by a system of equations.

I am going to say that:

x is the number of hot dogs that Barry ate.

y is the number of hot dogs that Andy ate.

z is the number of hot dogs that Carl ate.

The three ate a total of 103

So
`x + y + z = 103`

Andy ate 5 more than Barry

So
`y = x + 5`

Carl ate 10 less than Barry.

So
`z = x - 10`

How many did each eat?

`x + y + z = 103`

`x + x + 5 + x - 10 = 103`

`3x = 108`

`x = 36`

Barry ate 36 hot dogs.

Andy at 36+5 = 41 hot dogs.

Carl ate 36-10 = 26 hot dogs.