Multiple choice

Patricia's present age is 5 years more than Hilary's present age. The difference between the squares of their age, 3 years ago, was 25 years. What will be Hilary's age five years from now?

  1. 35 years

  2. 30 years

  3. 25 years

  4. 8 years

  5. 5 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Hilary's age be H, Patricia's age be H + 5. Three years ago, ages were H - 3 and H + 2. (H + 2)^2 - (H - 3)^2 = 25. (H^2 + 4H + 4) - (H^2 - 6H + 9) = 25. 10H - 5 = 25. 10H = 30, H = 3. Hilary's age 5 years from now = 3 + 5 = 8.

AI explanation

Let Hilary's present age be H, making Patricia's present age H + 5. Three years ago, the difference between the squares of their ages was 25, giving the equation (H + 2)^2 - (H - 3)^2 = 25. Using the difference of squares identity, this becomes 5 multiplied by the quantity 2H minus 1 equals 25, so 10H - 5 = 25, which means H = 3. Hilary's age five years from now will be 3 + 5, resulting in 8 years.

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