A painter bought \(16\) gallons of paint, just enough to cover two rooms. One is twice the size of the other and requires three coats of paint. The smaller room requires only two coats. Then the cilent decided not to paint the smaller room after all.

Let \(x\) be the number of gallons it takes for one coat of paint in the large room and \(y\) for the small room. How many gallons of paint will be left?

SpaceModo
Dec 25, 2017

#1**+1 **

Since **1x** coat of paint on the larger room requires **½x** as much for the smaller room,

therefore **2x** gallons for 2 coats on the larger room** = ½ x 2 =1y** gallons for the smaller room. But he decided not to paint the smaller room. So, we have:

A ratio of 3 to 1 gallons required to paint 3 coats for the larger room and 2 coats for the smaller room. So:

**3/{3+1} x 16 =12 gallons** required to paint the larger room 3 coats, or 12/3 =**4 gallons per coat**. The remaining 4 gallons would have been for the smaller room, or** 4/2 = 2 gallons per co**at.

So, he obviously has: **16 -12 = 4 gallons left**.

Guest Dec 25, 2017

#2**+1 **

Our guest has assumed that the smaller room takes half as much paint as the large one.

This probably IS what the question intended

BUT it actually implies that the larger room has twice as much volume, not twice as much surface area on the walls. I do not think you have enough information to answer the question based on volume though.

Melody
Dec 26, 2017

#3**+2 **

16 gal cover both rooms

And a total of 5 coats of paint are required for both rooms.....so.....each coat must require 16/5 gal

And since we are only painting the large room....only 3 coats *(16/5) gal per coat = 48/5 gal will be used

So.....the amount left is

16 - 48/5 =

80/5 - 48/5 =

32/5 gal

CPhill
Dec 26, 2017