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
Linear equation:
1
4
a +
1
3
a + 8 = 22
Make the writing short
Answers
GPT-4o mini
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**.
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**.