 Diego’s 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 an equation to find the ages of Diego and his sister.

Let Diego's age be represented by \( D \), and his sister's age by \( S \).

From the problem, we have two pieces of information:

1. Diego's sister is twice his age minus 9 years:
   \[
   S = 2D - 9
   \]

2. Diego's sister is also as old as half the sum of the ages of Diego and his two 12-year-old twin brothers:
   \[
   S = \frac{1}{2} \left( D + 12 + 12 \right) = \frac{1}{2} (D + 24)
   \]

Now, we can set up the system of equations:

1. \( S = 2D - 9 \)
2. \( S = \frac{1}{2} (D + 24) \)

To find Diego's age, set these two expressions for \( S \) equal to each other:

\[
2D - 9 = \frac{1}{2} (D + 24)
\]

This is the equation that can be used to solve for Diego's age \( D \).

Do you want me to solve it, or would you like to try it on your own? 

### Related questions:
1. How old is Diego based on the equation?
2. What would be the equation if his sister were 3 times Diego's age minus 5 years?
3. How would the solution change if the twins were 10 years old instead of 12?
4. What if Diego's sister was only 1 year younger than Diego? How would that affect the equation?
5. Could the system of equations be different if more siblings were involved?

**Tip:** Always ensure to isolate variables carefully to avoid algebraic mistakes when setting up equations.

Diego’s 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 an equation to find the ages of Diego and his sister.

Learn how to solve for Diego’s age using algebraic equations. The problem involves setting up a system of linear equations based on the relationship between Diego, his sister, and his 12-year-old twin brothers. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation