Multiple choice

Five years ago, Emma was one-fourth as old as Liam. Five years from now, Liam will be three times as old as Emma. What is the ratio of Emma's present age to Liam's present age?

  1. 1 : 7

  2. 5 : 17

  3. 12 : 17

  4. 15 : 17

  5. 17 : 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let E and L be present ages. (E-5) = 1/4(L-5) => 4E - 20 = L - 5 => L = 4E - 15. (L+5) = 3(E+5) => L + 5 = 3E + 15 => L = 3E + 10. Equating: 4E - 15 = 3E + 10 => E = 25. Then L = 3(25) + 10 = 85. Ratio E/L = 25/85 = 5/17.

AI explanation

Let Emma's present age be E and Liam's present age be L. The first condition gives E - 5 = (1/4)(L - 5), which simplifies to L = 4E - 15. The second condition gives L + 5 = 3(E + 5), which simplifies to L = 3E + 10. Setting the equations equal gives 4E - 15 = 3E + 10, so E = 25. Substituting E into the second equation gives L = 3(25) + 10 = 85. The ratio of Emma's present age to Liam's present age is 25 : 85, which simplifies to 5 : 17.

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