SOLUTION: The difference of two numbers is 11. The second is 8 less than 2 times the first. What are two numbers?

Question 71829: The difference of two numbers is 11. The second is 8 less than 2 times the first. What are two numbers?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let A represent the first number and B represent the second number.
.
In the problem the first sentence says that difference in these two numbers is 11. Therefore,
you can write the equation for this difference as:
.
A - B = 11
.
The second sentence says the second number (B) is 8 less than 2 times the first.
.
Two times the first is 2A and 8 less than that is, therefore, 2A - 8. Since this is to
equal the second (B) we can write the equation:
.
2A - 8 = B
.
Notice that from this second equation we have a value for B in terms of A. Let's take
the left side of this equation (that is take 2A - 8) and plug it into our first equation
in place of B. When we do the first equation becomes:
.
A - (2A - 8) = 11
.
Clear the parens by changing the terms inside to get:
.
A - 2A + 8 = 11
.
Combine the A terms to get:
.
-A + 8 = 11
.
Subtract 8 from both sides to get rid of it on the left side:
.
-A = 3
.
Multiply both sides by -1 and the answer for A is:
.
A = -3
.
Then you can take this value and substitute is for A in either of our two original
equations.
.
Let's substitute it into the first equation of A - B = 11. When you do you get:
.
-3 - B = 11
.
Add + 3 to both sides to get rid of the -3 on the left side:
.
-B = 14
.
And multiply both sides by -1 to solve for B. The result is:
.
B = -14
.
As a further check is -14 actually 8 less than 2 times (-3). It is and the answer
checks.
.
Hope this helps you to see how to work the problem. The big trick to problems such as
these is to analyze the words and translate them into correct equations. The rest is
straightforward math.

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