Question 422332: John is twenty years younger than Amy, and in five years' time he will be half her age. What is John's age now? Found 2 solutions by ewatrrr, algebrahouse.com:Answer by ewatrrr(24785) (Show Source):
Hi
John is twenty years younger than Amy
Let x and (x-20)represent Amy's and John's age NOW
Question states*** in 5 yrs...
(x-20) + 5 = (1/2)(x+5)
Solving for x
1/2x = 5/2 + 15
x = 5 + 30
x = 35, Amy's age now. John is now 15. (35-15)
CHECKING our Answer***in 5 yrs...
20 = (1/2)40
You can put this solution on YOUR website! "John is twenty years younger than Amy, and in five years' time he will be half her age. What is John's age now?"
x = Amy's age now
x - 20 = John's age now
x + 5 = Amy's age in 5 years
x - 15 = John's age in 5 years
x - 15 = 1/2(x + 5) {in five years, he will be half her age}
2x - 30 = x + 5 {multiplied entire equation by 2 to clear fraction}
2x = x + 35 {added 30 to both sides}
x = 35 {subtracted x from both sides}
x - 20 = 15 {substituted 35, in for x, into x - 20}
