Application problem

Question

Bob makes $4/hr more than Al, but only half of what Fred makes. Bob and Al work together for 10 hours and still make $12 less than Fred makes in 9 hours. What does Fred make per hour? I have to use an algebraic equation.

Answer 1

Hi Liz,

 

We have to translate the English into math. . .

 

Let X = Al's hourly salary

 

Bob makes $4/hr more than Al--> X + 4 = Bob's salary

 

Bob makes half of Fred's salary-->2(X + 4) = Fred's salary

 

Bob and Al work together for 10 hours--> 10(X + X+ 4)

 

and make $12 less than Fred makes in 9 hours--> 10(2X + 4) = (9)(2)(X + 4) - 12

 

Multiply out what's inside the parentheses--> 20X + 40 = 18X + 72 -12

 

Combine like terms--> 2X = 20

 

X = 10 = Al's hourly salary

 

Then Fred makes 2(X + 4) = 2(14) = $28 per hour.

 

Now you can figure out what Bob makes and plug the numbers back into the question to make sure they're correct.

 

Have fun.

 

Dan