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. ( 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
0 + 22h =77 22h =77 22h/22 =77/22 Divide each side by 22 h = 3.5 = 3 2 Danny was charged for 3 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. ( The source for the problem statement is: Intermediate AlgebraFor College Students by Jerome E. Kaufman |

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