remon rented a sprayer and a genarator. On his first job, he used each peice of equipment for 6 hours at a total cost of $90. On his second job,he used the sprayer for 4 hours and the genarator for 8 hours at the cost of $100. what was the hourly cost of each peice of equipment?
We are trying to find the hourly cost of the sprayer and the hourly cost of the generator. These are unknown.
From the cost of the first job, we know that:
6 hours of sprayer use + 6 hours of generator use = $90
To find out what it would cost for 1 hour of sprayer use and 1 hour of generator use, divide both sides of the equation by 6. We get:
1 hour of sprayer use + 1 hour of generator use = $15
Now rearrange this equation to find out how much 1 hour of sprayer use costs:
1 hour of sprayer use = $15 - 1 hour of generator use
From the cost of the second job, we know that:
4 hours of sprayer use + 8 hours of generator use = $100
Subsitute in our equation for the cost of 1 hour of sprayer use:
4 x ($15 - 1 hour of generator use) + 8 hours of generator use = $100
Multiply this out:
$60 - 4 hours of generator use + 8 hours of generator use = $100
Solve the equation:
4 hours of generator use = $40
1 hour of generator use = $10
Therefore:
1 hour of sprayer use = $5
Hope this helps,
A Tutor
To summarize:
1. Start by setting up equations based on the information given.
2. Divide both sides of the equation by the number of hours used to find the cost per hour of each equipment.
3. Rearrange the equation to isolate the hourly cost of one equipment.
4. Substitute this equation into the equation from the second job to find the cost per hour of the other equipment.
5. Solve the equation to determine the cost per hour of the second equipment.
6. Verify the solutions by substituting them back into the original equations.