Kamal is 17 years older than Gina, who is 3 years younger than Rachelle. If their total ages equal 77, how old is Gina?

To determine Gina's age, we start by translating the relationships into algebraic expressions based on the information provided:

1. Let Gina's age be represented as ( G ).

2. Since Kamal is 17 years older than Gina, Kamal's age can be expressed as ( K = G + 17 ).

3. Gina is 3 years younger than Rachelle, so Rachelle's age can be expressed as ( R = G + 3 ).

Now we know their total ages sum to 77, thus we can set up the equation incorporating all their ages:

[

G + (G + 17) + (G + 3) = 77

]

Combining like terms, we have:

[

3G + 20 = 77

]

To isolate ( G ), we first subtract 20 from both sides:

[

3G = 57

]

Then, divide by 3:

[

G = 19

]

This means Gina is 19 years old.

Understanding why this answer is correct lies in verifying that substituting ( G ) back into the relationships holds true with the total. If Gina is 19, Kamal would