Multiple choice

If the ratio of the ages (in years) of x and y, 8 years ago, is 7 ; 6, then which of the following can be the sum of their ages 8 years from now?

  1. 82

  2. 97

  3. 75

  4. 94
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let ages 8 years ago be 7k and 6k. Current ages are 7k+8 and 6k+8. Ages 8 years from now are 7k+16 and 6k+16. The sum is 13k+32. Testing values for k, if k=5, sum is 97. If k=4, sum is 84; if k=6, sum is 110.

AI explanation

Let the ages 8 years ago be 7x and 6x, making their present ages 7x + 8 and 6x + 8. Their ages 8 years from now will be 7x + 16 and 6x + 16, giving a combined sum of 13x + 32. Testing the given options, only 97 can be formed by an integer value of x: setting 13x + 32 = 97 gives 13x = 65, so x = 5, which fits perfectly.

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