Multiple choice

x years ago, Cory was one-fifth as old as Tom. x years from now, Tom will be twice as old as Cory. What is the ratio of Cory's present age to Tom's present age?

  1. 1 : 2

  2. 3 : 5

  3. 5 : 13

  4. 5 : 9

  5. 11 : 15
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let C and T be current ages. (C-x) = 1/5(T-x) => 5C - 5x = T - x => 5C - T = 4x. (T+x) = 2(C+x) => T + x = 2C + 2x => T - 2C = x. Substitute x: 5C - T = 4(T - 2C) => 5C - T = 4T - 8C => 13C = 5T. Ratio C/T = 5/13.

AI explanation

Let the present ages of Cory and Tom be C and T, giving the past equation C - x = (T - x) divided by 5 and the future equation T + x = 2(C + x). Rearranging the first equation gives 5C - T = 4x, and rearranging the second gives 2C - T = -x. Multiplying the second equation by 4 yields 8C - 4T = -4x, and adding this to the first equation yields 13C - 5T = 0, so the ratio of their present ages is 5 : 13.

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