Math Is Easy - Use Algebra To Solve Word Problem 3!

Danny received a car repair bill for $106. This included$23 for parts, $22 per hour for each hour of labor, and $6 for taxes. Findthe number of hours of labor. (Note 1)

Let h represent the number of hours of labor. Then 22hrepresents the total charges for labor. We can use a guideline of charge forparts plus charge for labor plus tax equals the total bill to set up thefollowing equation.

23(parts) + 22h(labor) + 6(tax) = 106

We can restate this as:

23 + 22h + 6 = 106

Solve this equation

23 + 22h + 6 =106

29 + 22h = 106 Add the common terms

29 + 22h = 106

-29= -29Subtract 29 from each side

0 + 22h =77

22h =77

22h/22 =77/22 Divide each side by 22

h = 3.5 = 3 1

2

Danny was charged for 3 1 hours of labor

2

Now we substitute the solutionfor h into the original equation to see if it works.

23 + 22h + 6 = 106

23 + 22(3.5 ) + 6 = 106

23 + 77 + 6 = 106

106 = 106

We must also see if the solution works in theoriginal problem statement.

Danny received a car repair bill for $106. This included$23 for parts, $22 per hour for each hour of labor, and $6 for taxes.

Danny received a car repair bill for $106. This included$23 for parts, $22 per hour for each hour of labor ($22 X 3.5), and $6 fortaxes.

Danny received a car repair bill for $106. This included$23 for parts, $22 per hour for each hour of labor ($77), and $6 for taxes.

106 = 23 + 77 + 6

We have just solved a first degree equation.

(Note1)

The source for the problem statement is:

Intermediate AlgebraFor College Students by Jerome E. Kaufman


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