To solve the equation:

\[
\frac{7y}{8} + \frac{3y}{5} = \frac{11}{2}
\]

### Step 1: Find a common denominator for the fractions on the left side.

The denominators are 8 and 5. The least common denominator (LCD) is 40.

- For \(\frac{7y}{8}\), multiply the numerator and the denominator by 5:
  \[
  \frac{7y}{8} = \frac{7y \times 5}{8 \times 5} = \frac{35y}{40}
  \]
  
- For \(\frac{3y}{5}\), multiply the numerator and the denominator by 8:
  \[
  \frac{3y}{5} = \frac{3y \times 8}{5 \times 8} = \frac{24y}{40}
  \]

### Step 2: Add the fractions.

\[
\frac{35y}{40} + \frac{24y}{40} = \frac{35y + 24y}{40} = \frac{59y}{40}
\]

So, the equation becomes:

\[
\frac{59y}{40} = \frac{11}{2}
\]

### Step 3: Cross-multiply to solve for \( y \).

\[
59y \times 2 = 11 \times 40
\]

\[
118y = 440
\]

### Step 4: Solve for \( y \).

\[
y = \frac{440}{118} = \frac{220}{59}
\]

So, \( y = \frac{220}{59} \).

Would you like more details or have any questions?

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Here are 5 related questions:

1. How do you find the least common denominator (LCD) of two fractions?
2. How do you solve linear equations with fractions?
3. What are some methods to simplify complex fractions?
4. How can cross-multiplication be used to solve equations involving fractions?
5. How do you check the solution of an equation?

**Tip:** Always simplify fractions in the final answer to their lowest terms to make calculations easier to understand.

Learn how to solve the equation involving fractions: 7y/8 + 3y/5 = 11/2. This problem requires finding a common denominator, adding fractions, and using cross-multiplication to find the solution. Suitable for high school students studying algebra and fractions.

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