Multiple choice

Elisa is $3$ years older than her brother Joseph. If the product of their ages is $10$. Find the age of Elisa.

  1. $3$ years
  2. $4$ years
  3. $5$ years
  4. $6$ years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Joseph's age be x, then Elisa's age is x + 3. The product of their ages is x(x + 3) = 10, which simplifies to x^2 + 3x - 10 = 0. Factoring gives (x + 5)(x - 2) = 0, so x = 2 (since age must be positive). Elisa's age is 2 + 3 = 5.

AI explanation

Let Joseph's age be x years, which makes Elisa's age x + 3 years. The product of their ages is x times the quantity x + 3 equals 10, which expands to the quadratic equation x squared plus 3x minus 10 equals 0. Factoring this equation gives x + 5 times x minus 2 equals 0, so x = 2 because age must be positive. Adding 3 to Joseph's age gives Elisa's age as 5 years.

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