The given equation is:

\[
\frac{x}{10} + \frac{y}{5} = 15
\]

To solve for \( x \) and \( y \), we can simplify and rearrange it.

### Step 1: Clear the denominators
Multiply the entire equation by 10 (the least common denominator of 10 and 5) to eliminate the fractions:

\[
10 \times \left( \frac{x}{10} + \frac{y}{5} \right) = 10 \times 15
\]

This simplifies to:

\[
x + 2y = 150
\]

### Step 2: Rearrange (if solving for one variable in terms of the other)
You can express one variable in terms of the other. For example, solving for \( x \) in terms of \( y \):

\[
x = 150 - 2y
\]

Alternatively, you can solve for \( y \) in terms of \( x \):

\[
2y = 150 - x
\]
\[
y = \frac{150 - x}{2}
\]

This gives you two ways to express the relationship between \( x \) and \( y \). You can substitute one variable's value if given further information.

Would you like to solve for specific values of \( x \) and \( y \), or do you have additional conditions?

---

### Related Questions:
1. What are the solutions for \( x \) and \( y \) if another equation is provided?
2. How would graphing the equation \( \frac{x}{10} + \frac{y}{5} = 15 \) help visualize the solutions?
3. What is the geometric meaning of \( x + 2y = 150 \)?
4. Can this system represent real-life scenarios like cost, speed, or mixture problems?
5. How does solving by substitution work for such linear equations?

### Tip:
When solving linear equations, multiplying through by the least common denominator is a quick way to eliminate fractions and simplify the process.

Explore the step-by-step solution for solving the linear equation x/10 + y/5 = 15. Learn how to simplify fractions, clear denominators, and express one variable in terms of another. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation