Let's solve the equation step by step.

We need to solve for the unknown value, which we'll denote as \( x \).

The equation given is:
\[
8 \frac{1}{4} + 60\% \text{ of } \frac{6}{5} = 15 - x
\]

### Step 1: Convert mixed number to an improper fraction
First, convert \( 8 \frac{1}{4} \) to an improper fraction:
\[
8 \frac{1}{4} = \frac{8 \times 4 + 1}{4} = \frac{33}{4}
\]

### Step 2: Calculate 60% of \(\frac{6}{5}\)
To find 60% of \(\frac{6}{5}\), multiply:
\[
60\% \times \frac{6}{5} = \frac{60}{100} \times \frac{6}{5} = \frac{3}{5} \times \frac{6}{5} = \frac{18}{25}
\]

### Step 3: Add the two fractions
Now, add the two fractions \( \frac{33}{4} \) and \( \frac{18}{25} \):
\[
\text{To add these, find a common denominator.}
\]
The least common denominator (LCD) of 4 and 25 is 100.

Convert both fractions to have a denominator of 100:
\[
\frac{33}{4} = \frac{33 \times 25}{4 \times 25} = \frac{825}{100}
\]
\[
\frac{18}{25} = \frac{18 \times 4}{25 \times 4} = \frac{72}{100}
\]
Now, add the two fractions:
\[
\frac{825}{100} + \frac{72}{100} = \frac{897}{100} = 8.97
\]

### Step 4: Set up the equation and solve for \( x \)
The equation now becomes:
\[
8.97 = 15 - x
\]
To solve for \( x \), subtract 8.97 from both sides:
\[
x = 15 - 8.97 = 6.03
\]

So, the value of \( x \) is **6.03**.

Do you want more details or have any questions? Here are 5 related questions that expand on this concept:

1. How do you find the least common denominator (LCD) of two fractions?
2. What is the general process for solving an equation involving fractions?
3. How can you convert percentages to fractions for calculation?
4. What are mixed numbers, and how do you convert them to improper fractions?
5. How can you verify the solution for \( x \) in this equation?

**Tip:** When working with fractions and percentages, converting everything to a common format (like improper fractions) simplifies the arithmetic.

Learn how to solve the equation 8 1/4 + 60% of 6/5 = 15 - x step-by-step. This problem involves fractions, percentages, and basic algebraic operations. Suitable for students in Grades 6-8.

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