https://file.aiquickdraw.com/mathbot/file/1725398824252rajlhab1.jpg

To solve for \( x \) in terms of \( y \) from the given ratio, we start with the equation provided:

\[
\frac{5x - 5}{5y + 2} = \frac{1}{5}
\]

### Step 1: Cross-Multiply

Cross-multiply to eliminate the fractions:

\[
5(5x - 5) = 1(5y + 2)
\]

### Step 2: Distribute and Simplify

Distribute the constants on both sides:

\[
25x - 25 = 5y + 2
\]

### Step 3: Solve for \( x \)

Add 25 to both sides to isolate the term involving \( x \):

\[
25x = 5y + 27
\]

Now, divide both sides by 25 to solve for \( x \):

\[
x = \frac{5y + 27}{25}
\]

So, the expression for \( x \) in terms of \( y \) is:

\[
\boxed{x = \frac{5y + 27}{25}}
\]

Would you like more details or have any questions? 

Here are five related questions you might consider:

1. How would you solve the equation if the ratio was different, say \( 2:3 \) instead of \( 1:5 \)?
2. What is the impact on \( x \) if \( y \) is doubled?
3. How do you verify if the solution for \( x \) is correct?
4. Can you express \( y \) in terms of \( x \) based on the initial equation?
5. How does the solution change if the constant term in the numerator or denominator was altered?

**Tip:** Always check your final answer by substituting it back into the original equation to ensure it satisfies the given conditions.

The ratio 5x - 5 : 5y + 2 is equal to 1 : 5. Express x in terms of y.

Learn how to solve the ratio 5x - 5 : 5y + 2 = 1 : 5 by expressing x in terms of y. This detailed step-by-step guide uses algebraic concepts, including cross-multiplication, to simplify and solve the problem, suitable for Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation