SOLUTION: The difference of two numbers is 7. The second is 7 less than 2 times the first. What are the two numbers?

Question 111467: The difference of two numbers is 7. The second is 7 less than 2 times the first. What are the two numbers?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You need to first express the problem symbolically. First thing you need are symbols for the two numbers, so let's call them and .
:
The first fact we know is that the difference of these two numbers is 7. So, let's call the larger of the two numbers, so we can write
:
Our next fact says "The second is 7 less than 2 times the first." So let's write:

:
Since the second equation gives us an expression for directly, let's just substitute into the first equation:
:

:
Add 7 to both sides and collect terms to get:
:

:
Now put this value back into equation 1:
:
, so

:
Last step, check your answer.
:
, and
. Since both of those statements are true, the answer checks.

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