Respuesta :
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 = [tex]\frac{x}{2}[/tex] ---------------------------------------(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 + [tex]\frac{x}{2}[/tex] + 2x = 42
Multiply through by 2
2x + x + 4x = 84
7x = 84
Divide both-side of the equation by 7
[tex]\frac{7x}{7}[/tex] = [tex]\frac{84}{7}[/tex]
x = 12
Therefore, Gina is 12 years old
