Question 1152572
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