Question

Describe the steps you used to solve the equation and find the amount of Carrie’s allowance.
Linear equation: 
1
4
a +
1
3
a + 8 = 22 Make the writing short

Answer 1

To solve the equation \(\frac{1}{4}a + \frac{1}{3}a + 8 = 22\):

1. **Combine like terms**: Find a common denominator for \(\frac{1}{4}\) and \(\frac{1}{3}\), which is 12. Rewrite the fractions:
\[
\frac{1}{4}a = \frac{3}{12}a, \quad \frac{1}{3}a = \frac{4}{12}a
\]
So, the equation becomes:
\[
\frac{3}{12}a + \frac{4}{12}a + 8 = 22
\]

2. **Combine the fractions**:
\[
\frac{7}{12}a + 8 = 22
\]

3. **Isolate the variable**: Subtract 8 from both sides:
\[
\frac{7}{12}a = 14
\]

4. **Solve for \(a\)**: Multiply both sides by \(\frac{12}{7}\):
\[
a = 14 \times \frac{12}{7} = 24
\]

Thus, Carrie's allowance is **$24**.