Describe the steps you used to solve the equation and find the amount of Carrie’s allowance.

Question

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.