SOLUTION: Mr. McCaffery decides to paint the ceiling and the walls of a room. He spends $120 on 2 gallons of paint for the ceiling and 4 gallons of paing for the walls. Then he decides to pa
Question 723161: Mr. McCaffery decides to paint the ceiling and the walls of a room. He spends $120 on 2 gallons of paint for the ceiling and 4 gallons of paing for the walls. Then he decides to paint a different room with the same kind of ceiling and wall paint. Write a system of linear equations that model the situation. A gallon of ceiling paint costs $3 more than a gallon of wall paint. What is the cost of one gallon of each type of paint? Answer by solver91311(24713) (Show Source):
There is no mention of the amount of paint required to do either the ceiling or the walls in the second room, so let be the number of gallons of ceiling paint that costs dollars per gallon and be the number of gallons of wall paint that costs dollars per gallon. Let be the total cost of paint for the second room.
The equation that models the first room is:
The equation that models the second room is:
Knowing the cost relationship between the two types of paint allows us to write:
Then by substitution:
From which you can determine the cost of the ceiling paint. Using the cost of the ceiling paint, that is to say , you can then subtract 3 to determine the cost of the wall paint, that is: .
Once you know the costs you can plug those numbers into:
to develop a formula for any size room where the same types of paint are used.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
