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. Find the number of hours of labor. (Note 1)

 

Let h represent the number of hours of labor. Then 22h represents the total charges for labor. We can use a guideline of “charge for parts plus charge for labor plus tax equals the total bill” to set up the following 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                  = -29 Subtract 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 solution for 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 the original  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 for taxes.

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.

 

(Note 1)

The source for the problem statement is:

“Intermediate Algebra  For College Students” by Jerome E. Kaufman

 


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