Question

1. reasoning diegos sister is twice his age minus 9 years. she is also as old as half the sum of the ages of diego and both of his 12 - year - old twin brothers. write and solve an equation to find the ages of diego and his sister.

Explanation:

Step1: Let Diego's age be $x$.

Let Diego's age be $x$ years. His sister's age can be expressed in two - ways. First way: His sister's age $y = 2x−9$. Second way: His twin brothers are 12 years old each. The sum of Diego and his twin - brothers' ages is $x + 12+12=x + 24$. So his sister's age $y=\frac{1}{2}(x + 24)$.

Step2: Set up the equation.

Since both expressions represent his sister's age, we set them equal to each other: $2x−9=\frac{1}{2}(x + 24)$.

Step3: Solve the equation.

First, multiply both sides of the equation by 2 to get rid of the fraction: $2(2x−9)=x + 24$. Expand the left - hand side: $4x-18=x + 24$. Subtract $x$ from both sides: $4x-x-18=x - x+24$, which simplifies to $3x-18 = 24$. Add 18 to both sides: $3x-18 + 18=24 + 18$, so $3x=42$. Divide both sides by 3: $x = 14$.

Step4: Find his sister's age.

Substitute $x = 14$ into the equation for his sister's age. Using $y = 2x−9$, we have $y=2\times14−9=28 - 9=19$.

Answer:

Diego is 14 years old and his sister is 19 years old.