Question

Explaining the Properties of Equality

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

Linear equation:  14 a +  13 a + 8 = 22

Answer 1

Equation: 14a + 13a + 8 = 22

1. Combine like terms (use distributive/like-terms rule):
14a + 13a = (14 + 13)a = 27a.
So the equation becomes 27a + 8 = 22.

2. Use the Subtraction Property of Equality (subtract 8 from both sides):
27a + 8 − 8 = 22 − 8 → 27a = 14.

3. Use the Division Property of Equality (divide both sides by 27):
a = 14/27.

Check: 14(14/27) + 13(14/27) + 8 = 27(14/27) + 8 = 14 + 8 = 22, so the solution is correct.

If a is dollars, Carrie’s allowance is 14/27 dollar ≈ $0.52.