Question: Solve for $w$.
$\frac{w}{8} + \frac{w}{12} = \frac{5}{8}$
Simplify your answer as much as possible.
$w = [ ]$
1. **State the problem:** Solve for $w$ in the equation $$\frac{w}{8} + \frac{w}{12} = \frac{5}{8}$$.
2. **Find a common denominator for the fractions on the left side:** The denominators are $8$ and $12$. The least common denominator (LCD) is $24$.
3. **Rewrite each fraction with denominator $24$:**
$$\frac{w}{8} = \frac{3w}{24}$$
$$\frac{w}{12} = \frac{2w}{24}$$
4. **Combine the fractions:**
$$\frac{3w}{24} + \frac{2w}{24} = \frac{5w}{24}$$
5. **Rewrite the equation:**
$$\frac{5w}{24} = \frac{5}{8}$$
6. **Solve for $w$ by cross-multiplying:**
$$5w \times 8 = 5 \times 24$$
$$40w = 120$$
7. **Divide both sides by $40$ to isolate $w$:**
$$w = \frac{120}{40}$$
8. **Simplify the fraction:**
$$w = \frac{\cancel{120}^{3} \times 40}{\cancel{40}^{1} \times 40} = 3$$
**Final answer:**
$$w = 3$$