Manhattan Challenge Problem of the week ! - 13/26/07

x years ago, Cory was one fifth as old as Tania. In x years, Tania will be twice as old as Cory. What is the ratio of Cory's current age to Tania's current age?

(A) 7:23
(B) 9:17
(C) 5:13
(D) 3:7
(E) 11:15

Answer : C

Use a chart to keep track of the ages in this problem:

	x years ago	NOW	in x years
Corey	C - x	C	C + x
Tania	T - x	T	T + x

Then write algebraic expressions to represent the information given in the problem:

x years ago, Cory was one fifth as old as Tania 5(C – x) = T – x 5C – 5x = T – x 5C – T = 4x

In x years, Tania will be twice as old as Cory 2(C + x) = T + x 2C + 2x = T + x T – 2C = x

Substitute T - 2C in for x in the first equation and solve:

5C - T = 4(T - 2C)
5C - T = 4T - 8C
13C = 5T

C/T = 5/18

The correct answer is C.