Question

Isaac has written down one integer two times and another integer three times. The sum of the five numbers is 100, and one of the numbers is 28. What is the other number?

Answer 1

8

Explanation:

Since we know that one integer is written two times, and the other is written three times, and we know the sum of all of them are 100, we can write an equation that represents this.

Call the integer written twice `x`, and the integer written three times `y`

`2x + 3y = 100`

We know one of the numbers (either `x` or `y`) is 28, so we should just use guess and check to determine which is which, and what the other number is.

If 28 is written twice, we could have the following:
`56 +3y = 100`
Which simplifies to
`3y = 44`

`44/3` is not an integer, and will be a fraction, so this cannot be the case.

On the other hand if 28 is written three times, we have the following:
`2x + 84 = 100`
Which simplifies to
`2x=16`

`16/2` can be simplified to equal 8, which is an integer and the other number.

Hope that helps