SOLUTION: Today Matt is 5 times the age of his cousin Kristin. In 4 years time, Kristin will be one third of Matt’s age. How old will Matt be when Kristin is 40 years old?

Question 1134744: Today Matt is 5 times the age of his cousin Kristin. In 4 years time, Kristin will be
one third of Matt’s age. How old will Matt be when Kristin is 40 years old?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let m equal the age of matt now.
let k equal the age of kristin now.

today matt is 5 times the age of kristin.

the formula for that is m = 5 * k.

in 4 years time, kristin will be one third the age of matt.

the formula for that is k + 4 = 1/3 * (m + 4)

in the second equation, replace m with 5 * k to get:

k + 4 = 1/3 * (5 * k + 4)

now that you have one unknown in one equation, you can solve for k.

start with k + 4 = 1/3 * (5 * k + 4)

simplify to get k + 4 = 5/3 * k + 4/3

subtract 4/3 from both sides of this equation to get k + 4 - 4/3 = 5/3 * k

subtract k from both sides of this equation to get 4 - 4/3 = 5/3 * k - k

multiply both sides of this equation by 3 to get 12 - 4 = 5 * k - 3 * k

combine like terms to get 8 = 2 * k

divide both sides of this equation by 2 to get 4 = k.

since k = 4, then m = 5 * k becomes m = 5 * 4 = 20.

kristin is 4 years old and matt is 20 years old today.

in 4 years, kristin will be 8 years old and matt will be 24 years old.

20 / 4 = 5, so matt is 5 * the age of kristin today.

8 / 24 = 1/3, so kkristin will be 1/3 the age of matt in 4 years.

kristin will be 40 years old in 40 - 4 = 36 years.

in 36 years, matt will be 20 + 36 = 56 years old.

your solution is that matt will be 56 years old when kristin is 40 years old.

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