SOLUTION: Two numbers have a difference of 10 and the sum of 34. What are the numbers?

Question 108952This question is from textbook Harcourt Math Practice Workbook
: Two numbers have a difference of 10 and the sum of 34. What are the numbers?

This question is from textbook Harcourt Math Practice Workbook

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Call the two unknown numbers x and y.
.
Since their difference is 10 you can write the equation:
.
x - y = 10
.
And since their sum is 34 you can write the equation:
.
x + y = 34
.
Write the two equations one above the other:
.
x - y = 10
x + y = 34
.
Note that if you add the two equations vertically in columns that the -y of the top equation
will cancel the +y of the bottom equation. So, adding vertically results in the x + x = 2x,
the two y terms cancel, and on the right side the 10 + 34 = 44
.
Therefore, the result of the addition is:
.
2x = 44
.
And if you divide both sides of this equation by 2 you get:
.
x = 22
.
Since x + y is to equal 34, then you can write:
.
22 + y = 34
.
Subtracting 22 from both sides of this equation results in:
.
y = 12
.
So the answer to this problem is that one of the numbers is 22 and the other is 12.
.
As a check, note that the difference of the two numbers is 22 - 12 = 10 and the sum of the
two numbers is 22 + 12 = 34, just as the problem says things should be.
.
Hope this helps you to understand the problem a little better.
.
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