Multiple choice

Amy is $5$ years older than her sister Julie. If the product of their ages is $6$. Find the age of Julie.

  1. $1$ year
  2. $2$ years
  3. $3$ years
  4. $4$ years
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A Correct answer
Explanation

Let Julie's age be x. Then Amy's age is x + 5. The product of their ages is x(x + 5) = 6, which simplifies to x^2 + 5x - 6 = 0. Factoring gives (x + 6)(x - 1) = 0, so x = 1 (since age must be positive).

AI explanation

Let Julie's age be y years, making Amy's age y + 5 years. Setting the product of their ages to 6 gives the equation y(y + 5) = 6, which rearranges to y squared plus 5y minus 6 equals 0. Solving this quadratic equation by factoring gives (y + 6)(y - 1) = 0, resulting in the valid positive root of 1. Julie is 1 year old.

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