SOLUTION: The sum of two numbers is 124, and three-fifths of one of the numbers exceeds the other by 36. What are the numbers?

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Question 657873: The sum of two numbers is 124, and three-fifths of one of the numbers exceeds the other by 36. What are the numbers?
Answer by colliefan(242)   (Show Source): You can put this solution on YOUR website!
If x and y are the numbers, then the statements in the problem can be written as:
x+y=124
3/5x=y-36

I would solve this system of equations by substitution. To do this, solve one of the equations for one variable (we'll do that in the first equation for y). That gives you an expression for x that uses the other variable. We will then substitute that into the other equation and solve for the only variable that will be left in that equation.
x+y=124
x+y-x=124-x
y+0=124-x
y=124-x
Substitute this into the second equation.
3/5x=y-36
3/5x=(124-x)-36
3/5x=88-x
3/5x+x=88-x+x
8/5x=88
5/8*8/5x = 88*5/8
x = 55

Substituting this value for x into either of the two original equations lets you calculate that y must be 69.
Substitute these values into both equations to make sure that they are really solutions.


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