Question

The larger of two integers is seven more than the smaller integer. Their sum is 49. Find the integers.

Answer 1

The two integers have values 28 and 21

Explanation:

This is a simultaneous equation problem. Let the two integers be represented by
`a` and
`b`.

The first part of the question can be represented by the following equation:

`a-b=7`

From the second part of the question, we know their sum is 49, which can be represented by:

`a+b=49`

Now, we need to manipulate the expressions to contain just one unknown value. If we add
`b` to both sides of the first equation we get:

`a=b+7`

Now we can substitute the value of
`a` for
`b+7` in the second equation:

`a+b=(b+7)+b=49`

Which we can then rearrange and solve for
`b`:

`2b +7=49\\2b=42\\b=21`

We can now use the value for
`b` in either of the two original equations for find the value of
`a`:

`a=b+7=(21)+7=28`.

We now have the the two values 28 and 21.

Note: To double check the answer, check if their sum is equal to 49:

`a+b=28+21=49`.