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:

Barry ate 36 hot dogs.

Andy at 36+5 = 41 hot dogs.

Carl ate 36-10 = 26 hot dogs.

Step-by-step 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.

Answer 2

Answer:Andy ate 41 hot dogs.

Barry ate 36 hot dogs.

Carl ate 26 hot dogs.

Step-by-step 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