Question

Mina is 7 years old. Her older sister is 3 more than 2 times Mina’s age. Mina’s younger sister is 8 less than twice her age. Mina’s mothers age is 10 more than twice of Mina’s sister’s age. Mina’s grandmother is all of the ages of Mina, her older sister, her younger sister, and her mother combined. How old is Mina’s grandmother?

Answer 1

Answer & Step-by-step explanation:

Let's start by defining some variables:

M = Mina's age

O = Mina's older sister's age

Y = Mina's younger sister's age

A = Mina's mother's age. We can now use the information given in the problem to set up a system of equations:

O = 2M + 3

Y = 2M - 8

A = 2Y + 10

Grandmother's age = M + O + Y + A

We can substitute the first three equations into the fourth equation to get:

Grandmother's age = M + (2M + 3) + (2M - 8) + (2(2M - 8) + 10)

Simplifying this expression, we get:

Grandmother's age = 9M + 9

Finally, we can substitute M = 7 (Mina's age) to get:

Grandmother's age = 9(7) + 9 = 72 Therefore, Mina's grandmother is 72 years old.

Hope it helps!