SOLUTION: Please help me solve this word problem. Matt's age is 40% of his father's age. Ten years from now, Matt's age will be 50% of his father's age. How old are Matt and his father

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Question 1152572: Please help me solve this word problem.
Matt's age is 40% of his father's age. Ten years from now, Matt's age will be 50% of his father's age. How old are Matt and his father now?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
let x = matt's age.
let y = matt's father's age.
you get x = .4 * y
that's the current relationship between their ages.
in ten years, matt's age will be 50% of his father's age.
you get x + 10 = .5 * (y + 10)
that's the relationship of their ages 10 years from now.
you have two equations that need to be solved simultaneously.
they are:
x = .4 * y
x + 10 = .5 * (y + 10)
replace x with .4 * y in the second equation to get:
.4 * y + 10 = .5 * (y + 10)
simplify to get:
.4 * y + 10 = .5 * y + 5
subtract .4 * y from both sides of the equation and subtract 5 from both sides of the equation to get:
10 - 5 = .5 * y - .4 * y
combine like terms to get:
5 = .1 * y
solve for y to get:
y = 5 /.1 = 50
that's his father's age today.
his age today is .4 * 50 = 20.
in 10 years, matt will be 30 and his father will be 60.
that means that matt's age will be .5 * his father's age at that time.
your solution is that matt is 20 and his father is 50 today.
today, 20/50 = .4
10 years from now, 30/60 = .5

Answer by MathTherapy(10555) (Show Source):
You can put this solution on YOUR website!

Please help me solve this word problem.
Matt's age is 40% of his father's age. Ten years from now, Matt's age will be 50% of his father's age. How old are Matt and his father now?

Let father's age be F
Then Matt's is .4F
We then get: .4F + 10 = .5(F + 10)
.4F + 10 = .5F + 5
.4F - .5F = 5 - 10
- .1F = - 5
F, or father is:
Take 40% or .4 of father's age to get Matt's age.
That's IT!! Nothing COMPLEX!