SOLUTION: The sum of two numbers is 39. One number is three more then half the other number. What is the larger number?

Question 450673: The sum of two numbers is 39. One number is three more then half the other number. What is the larger number?
Answer by blwinbbbles(106) (Show Source): You can put this solution on YOUR website!
Lets create equations from what we know:
Equation 1) the sum is 39 so: a + b = 39
Equation 2) one number is three more than half the other..so: a/2 + 3 = b
I would get rid of the fraction in equation 2 by multipling the equation by 2
2(a/2 + 3 = b)
a + 6 = 2b then I would set it up to show a single variable to equal the other
SO:
a + 6 = 2b subtract 6 from both sides
a = 2b - 6 now we can use this equation to substitute into equation 1
2b - 6 + b = 39
3b - 6 = 39 add 6 to both sides
3b = 45 divide both sides by 3
b = 15
Now that you know b, plug that into one of the equations and solve
a + 15 = 39 substract 15 from both sides
a = 24
So now you know that the two numbers are 15 and 24

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