Question

Victoria is five years younger than Danielle. Grace is 15 years younger than Danielle. Joseph is 4 years older than Grace. The sum of their ages is 69. How old is Grace?

A) 20 years old
B) 15 years old
C) 10 years old
D) 25 years old

Answer 1

By setting up and solving a system of linear equations based on the relationships between the ages, we find that Grace is 10 years old.

Step-by-step explanation:

The question requires solving a system of linear equations to find Grace's age. Let us denote Danielle's age as D. Therefore, Victoria's age will be D - 5 and Grace's age will be D - 15. Joseph is 4 years older than Grace, so Joseph's age is (D - 15) + 4 which simplifies to D - 11. The sum of their ages is given as 69, so the equation we can form is:

D + (D - 5) + (D - 15) + (D - 11) = 69.

Combining like terms gives us:

4D - 31 = 69.

Adding 31 to both sides gives us:

4D = 100,

and dividing by 4 gives us:

D = 25.

Since Grace is 15 years younger than Danielle, her age will be:

25 - 15 = 10.

So, Grace is 10 years old.