SOLUTION: Today, Paul is 27 years younger than his mother. In 5 years, Paul's she will be 1/4 of his mother's age. How old is Paul's mother today? Please help me answer this!

Question 1137573: Today, Paul is 27 years younger than his mother. In 5 years, Paul's she will be 1/4 of his mother's age. How old is Paul's mother today?
Please help me answer this!
Found 2 solutions by Theo, josmiceli:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = paul's mother's age.
paul is 27 years younger than his mother today, so his age is x - 27.
in 5 years,he will be 1/4 of his mother's age.
formula for that is x - 27 + 5 = 1/4 * (x + 5)
simplify to get x - 22 = 1/4 * (x + 5)
multiply both sides of this equation by 4 to get 4 * (x - 22) = x + 5.
simplify to get 4x - 88 = x + 5
subtract x from both sides of this equation and add 88 to both sides of this equation to get 4x - x = 88 + 5
combine like terms to get 3x = 93.
solve for x to get x = 93/3 = 31.

his mother is 31 years old today.
paul is 27 years younger, so paul is 31 - 27 = 4.
5 years from now, paul will be 9 and his mother will be 36.
9 is equal to 1/4 * 36 because 4 * 9 = 36.

solution looks good.
solution is that paul's mother is 31 years old today.

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = Paul's mother's age now
= Paul's age now
---------------------------------------------

Paul's mother is 31 now
--------------------------------
check:

OK

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