Multiple choice

Lisa's present age is 6 years more than Kevin's present age. Five years ago, the difference between the squares of their ages was 48 years. Quantity A: Lisa's age five years from now Quantity B: 16

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
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A Correct answer
AI explanation

Let Kevin's present age be k years, making Lisa's present age (k + 6) years. Five years ago, the difference between the squares of their ages was 48, giving the equation (k + 1)^2 - (k - 5)^2 = 48. Applying the algebraic identity a^2 - b^2 = (a - b)(a + b), we get (6)(2k - 4) = 48, which simplifies to 12k - 24 = 48 and yields k = 6. Lisa's present age is 12 years, so her age five years from now will be 17 years, making Quantity A greater.

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