Question

Compare Solution Methods for Two-Step Equations Quick Check 5 of 55 of 5 Items Question A window cleaner has enough supplies to clean 21 windows per office building on a certain number of buildings. They can also clean the windows of a school with 42

Answer 1

windows. The equation 21x + 42 = 105 represents the total number of windows the cleaner can clean.

To solve this equation, we can use two solution methods: algebraic method and substitution method.

1. Algebraic Method:
To solve the equation 21x + 42 = 105 using the algebraic method, we need to isolate the variable x.

Step 1: Subtract 42 from both sides of the equation:
21x + 42 - 42 = 105 - 42
21x = 63

Step 2: Divide both sides of the equation by 21 to solve for x:
x = 63/21
x = 3

Therefore, the cleaner can clean 3 office buildings.

2. Substitution Method:
To solve the equation 21x + 42 = 105 using the substitution method, we can solve for x by substituting the expression for the total number of windows into the equation.

Step 1: Substitute the expression for the total number of windows into the equation:
21x + 42 = 105
21x + 42 = 21(3)

Step 2: Simplify the equation:
21x + 42 = 63

Step 3: Subtract 42 from both sides of the equation:
21x + 42 - 42 = 63 - 42
21x = 21

Step 4: Divide both sides of the equation by 21 to solve for x:
x = 21/21
x = 1

Therefore, the cleaner can clean 1 office building.

Both methods yield different solutions for x. The algebraic method gives x = 3, while the substitution method gives x = 1. This discrepancy occurs because the substitution method assumes that the expression being substituted is equal to the equation, while the algebraic method solves the equation step by step to isolate the variable. In this case, the correct solution is x = 3 because the cleaner can clean 21 windows per office building.