SOLUTION: The sum of Gerald's age and Ben's age is 53. Five years ago, Gerald was 7 years more than one-half as old as ben. How old are they?

Question 1133520: The sum of Gerald's age and Ben's age is 53. Five years ago, Gerald was 7 years more than one-half as old as ben. How old are they?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
g = gerald's age now.
b = ben's age now.

the sum of their ages today is 53, therefore:

g + b = 53

5 years ago, gerald was 7 more than half ben's age, therefore:

g - 5 = 7 + 1/2 * (b - 5)

subtract 7 from both sides of the second equation to get:
g - 12 = 1/2 * (b - 5)
multiply both sides of this equation by 2 to get:
2g - 24 = b - 5
add 5 to both sides of this equation to get:
2g - 19 = b

in the first equation of b + g = 53, solve for b to get b = 53 - g.
replace b with 53 - g in the equation of 2g - 19 = b to get:
2g - 19 = 53 - g
add g to both sides of this equation and add 19 to both sides of this equation to get:
3g = 72
divide both sides of this equation by 2 to get:
g = 24.
since g + b = 53, solve for b to get:
b = 29

you have g = 24 and b = 29

g + b = 24 + 29 = 53 which is true.
g-5 = 7 + 1/2 * (b-5) becomes 24-5 = 7 + 1/2 * (29 - 5) which becomes 19 = 7 + 1/2 * 24 which becomes 19 = 7 + 12 which becomes 19 = 19 which is true.

the solution looks good.

the solution is gerald is 24 years old and ben is 29 years old.

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