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 the constants: Subtract 8 from both sides. \[ \frac{1}{4}a + \frac{1}{3}a = 14 \]

2. Find a common denominator: The least common multiple of 4 and 3 is 12. Rewrite the fractions: \[ \frac{3}{12}a + \frac{4}{12}a = 14 \]

3. Combine the fractions: \[ \frac{7}{12}a = 14 \]

4. Multiply both sides by the reciprocal of \( \frac{7}{12} \): \[ a = 14 \cdot \frac{12}{7} = 24 \]

Thus, Carrie’s allowance is $24.