Question

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

Answer 1

Answer:

The two integers have values 28 and 21

Step-by-step 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:

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