Multiple choice

The brother is older than his sister by 7 years. Five years ago, the product of their ages was 30. What was the age of the brother 5 years ago?

  1. 15 years

  2. 8 years

  3. 10 years

  4. 3 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the brother's age 5 years ago be x. Then the sister's age was x - 7. Their product was x(x - 7) = 30. Solving x^2 - 7x - 30 = 0 gives (x - 10)(x + 3) = 0. Since age must be positive, x = 10.

AI explanation

Let the brother's age 5 years ago be x years, making his sister's age x - 7 years at that time. The product of their ages gives the equation x * (x - 7) = 30, which expands to x^2 - 7x - 30 = 0. Factoring this quadratic equation gives (x - 10)(x + 3) = 0, and since age must be positive, x is 10 years.

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