Question

Gabriela is 5 years older than her sister Zorayda. If the product of their ages is 126,how old is Gabriela? (Please help me I’ve been stuck on this forever)

Answer 1

To find Gabriela's age, we solve the equation x(x + 5) = 126, where x is Zorayda's age, and find that Zorayda is 9 years old and Gabriela is 14 years old.

Step-by-step explanation:

Gabriela is 5 years older than her sister Zorayda. If the product of their ages is 126, we need to find out how old both sisters are, focusing on Gabriela’s age. We can create an equation to represent this situation where x is Zorayda's age and x + 5 is Gabriela's age. Therefore, the equation will be x(x + 5) = 126.

Now, we solve for x:

1. x^2 + 5x = 126
2. x^2 + 5x - 126 = 0
3. The factors of 126 that have a difference of 5 are 14 and 9.
4. So, we can rewrite the equation as (x - 9)(x + 14) = 0
5. Setting each factor equal to zero gives us two possible solutions for x: x = 9 or x = -14.
6. Since ages can't be negative, Zorayda's age is 9 years.
7. To find Gabriela's age, we add 5 to Zorayda's age, so Gabriela is 14 years old.