SOLUTION: 4. George is 12 years older than Jeannie. The sum of their ages in 5 years will be 50. How old is Jeannie now? a. Define the variables. b. Write an expression for the age

Question 87230: 4. George is 12 years older than Jeannie. The sum of their ages in 5 years will be 50. How old is Jeannie now?
a. Define the variables.

b. Write an expression for the age of George in terms of Jeannie's age.

c. Write an equation for the sum of their ages in 5 years from now.
d. Solve the equation for the age of Jeannie now.

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
George is 12 years older than Jeannie. The sum of their ages in 5 years will be 50. How old is Jeannie now?
a. Define the variables.
.
Just to help us remember what is what, let's use G to represent George's current age and
J to represent Jeannie's current age.
.
b. Write an expression for the age of George in terms of Jeannie's age.
.
The problem tells you that George is 12 years older than Jeannie. That means if you subtract
12 from George's age, the answer should be Jeannie's age. In equation form this would be:
.
G - 12 = J
.
Solve for G by adding 12 to both sides to get:
.
G = J + 12
.
c. Write an equation for the sum of their ages in 5 years from now.
.
Five years from now George's age will be G + 5 and Jeannie's age will be J + 5. The problem
tells you that the sum of these ages will be 50. In equation form this would be:
.
G + 5 + J + 5 = 50
.
By adding the two 5s on the left side this simplifies to:
.
G + J + 10 = 50
.
And subtracting 10 from both sides further simplifies this equation to:
.
G + J = 40
.
d. Solve the equation for the age of Jeannie now.
.
Start with the equation from part c:
.
G + J = 40
.
But way back in part b it is known that G = J + 12. Substitute the right side of this
equation in place of G and get:
.
J + 12 + J = 40
.
Add the two Js and the equation becomes:
.
2J + 12 = 40
.
Subtract 12 from both sides results in:
.
2J = 28
.
Divide both sides by 2 to solve for J and you get:
.
J = 28/2 = 14
.
This tells us that Jeannie is 14 years old at present.
.
That means that George, who is 12 years older, is 26 at present.
.
Five years from now, Jeannie will be 14 + 5 or 19 years old. And George will be 26 + 5
or 31 years old. The sum of their ages will be 19 + 31 which is 50, just as the problem
said it should be.
.
Hope this helps you to understand the problem.

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