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# Plato Classroom Question #11

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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?

Dec 25, 2017

#1
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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 coat.
So, he obviously has: 16 -12 = 4 gallons left.

Dec 25, 2017
#2
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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
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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

Dec 26, 2017