SOLUTION: the larger of two numbers is five times the smaller. if the difference is fifty-two, what are these numbers? thanks for helping out.

Question 124904: the larger of two numbers is five times the smaller. if the difference is fifty-two, what are these numbers? thanks for helping out.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let L represent the larger number and S represent the smaller number.
.
The problem first tells you that the Larger number is 5 times the Smaller number. In equation
form this becomes:
.
L = 5*S
.
Then the problem tells you that the difference of the two numbers is 52. In equation form
this is:
.
L - S = 52
.
But from the first equation you know that L equals 5S. So in the second equation you can
substitute 5S for L. When you do that substitution the second equation becomes:
.
5S - S = 52
.
Combine the two terms on the left side and the equation is reduced to:
.
4S = 52
.
Solve for S by dividing both sides of this reduced equation by 4 and you get:
.
S = 52/4 = 13
.
So now you know that the Smaller number is 13. And you also know that the Larger number is
5 times the Smaller number. Therefore, the larger number is 5*13 = 65
.
So now you know that the two numbers are 65 and 13. Notice that the difference in these
two numbers is 52, just as the problem said it should be.
.
Hope this helps you to understand the problem a little better.
.

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