Question

Gina is a certain age (g). Gina's older sister is twice Gina's age. Gina's brother is half Gina's age. The sum of their ages is 42. How old is Gina?

Answer 1

Answer:

Gina is 12 years old

Step-by-step explanation:

First,  we will have to write these statements mathematically and then solve.

Let Gina's age be x, let Gina's brother's age be y and let Gina's sister's age be z.

The second statement"Gina's older sister is twice Gina's age" can be mathematically written as: z =2 x ---------------------------(1)

The next statement "Gina's brother is half Gina's age" can be mathematically written as y = $\frac{x}{2}$ ---------------------------------------(2)

Then the next statement "the sum of their ages is 42" can be mathematically written as: x + y + z = 42 ----------------------------(3)

We can now proceed to solve;

Substitute equation (1) and equation(2) into equation (3)

x + y + z = 42

x +  $\frac{x}{2}$ + 2x = 42

Multiply through by 2

2x + x + 4x = 84

7x = 84

Divide both-side of the equation by 7

$\frac{7x}{7}$ = $\frac{84}{7}$

x = 12

Therefore, Gina is 12 years old