SOLUTION: 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 h

Algebra.Com
Question 999089: 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?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the trick is to make everything in terms of one of the variables.

let b = how much bob makes per hour.
let a = how much al makes per hour.
let f = how much fred makes per hour.

you are given that:

b = a+4
b = f/2
(b+a)*10 = f*9-12

make a and f in terms of b and you can then solve for b.

since b = a + 4, then a = b - 4

since b = f/2, then f = 2 * b

the equation you want to solve is:

(b+a)*10 = f*9-12

raplace a with b-4 and replace f with 2b, and you get:

(b + b - 4) * 10 = 2b * 9 - 12

simplify to get:

(2b-4)*10 = 18b - 12

simplify further to get:

20b - 40 = 18b - 12

subtract 18b from both sides of this equation and add 40 to both sides of this equation to get:

2b = 28

solve for b to get b = 14.

since a = b-4, then a = 10

since f = 2b, then f = 28

your numbers are:

b = 14
a = 10
f = 28

b = a + 4 becomes 14 = 10 + 4 which is true.
b = f/2 becomes 14 = 28/2 which is true.
(b+a)*10 = f*9-12 becomes (14+10)*10 = 28*9 - 12 which becomes:
24 * 10 = 28 * 9 - 12 which becomes:
240 = 252 - 12 which becomes:
240 = 240 which is true.

all givens are confirmed to be true when b = 14, a = 10, and f = 28.

those are your solutions.

you were asked what fred makes per hour.

your answer is that fred makes 28 dollars per hour.





Answer by MathTherapy(10549)   (Show Source): You can put this solution on YOUR website!

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?
Let Fred’s per-hour pay be F

Then Bob makes: , or  per hour

Also, Al makes:  per hour

We then get:  

5F + 5F – 40 = 9F – 12

5F + 5F – 9F = - 12 + 40

10F – 9F = 28

F, or amount Fred makes, per hour =  

RELATED QUESTIONS


Bob takes 3 hours to mow a lawn. Al takes 4 hours. If they work together how long will it  (answered by josgarithmetic,mananth)

. Bob takes 3 hours to mow a lawn. Al takes 4 hours. If they work together how long will... (answered by jim_thompson5910)

 Dan is twice as old as Bob and four times as old as Al.
· Charles is four years younger  (answered by ikleyn)

bob is 12 years less than triple als age if bobs and als age sum to 104 years how old are  (answered by Cromlix,stanbon)

Al makes $30 an hour. Bill makes $20 an hour. Bill joins Al on the job four hours after... (answered by jojo14344,alan22153)

You are on the island of knights and knaves, where (a) every local is either
a knight or  (answered by CPhill)

Al is 2 years older than Bob. Bob is 4 years younger than Carl. The sum of the three... (answered by stanbon)

Using a system of equations in two variables, solve the following:

Al and Bev traveled  (answered by josgarithmetic)

You have asked your boss for a raise. He tells you that you are already the highest paid... (answered by josmiceli)