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I have to paint one side of a wall.  The wall is 12 meters tall and 120 meters long.  Each gallon of paint covers 150 square feet. If a foot is approximately 0.3048 meters, then what is the smallest whole number of gallons I can buy and have enough paint to cover the whole wall?

 Jun 14, 2023
 #1
avatar+4 
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Hello,

 

To find the number of gallons needed to paint the wall, we need to calculate the total area of the wall in square meters and then convert it to square feet.

The wall is 12 meters tall and 120 meters long, so its total area is:

Area = height × length
= 12 meters × 120 meters
= 1440 square meters

To convert this area to square feet, we can use the conversion factor that 1 square meter is approximately equal to 10.764 square feet:  prepaidgiftbalance

Area (in square feet) = Area (in square meters) × 10.764
= 1440 square meters × 10.764
= 15,520.16 square feet

Now, we can calculate the number of gallons needed. We know that 1 gallon covers 150 square feet:

Number of gallons = Total area (in square feet) ÷ Coverage per gallon
= 15,520.16 square feet ÷ 150 square feet
≈ 103.47

Since we can't buy a fraction of a gallon, we need to round up to the nearest whole number. Therefore, you should buy at least 104 gallons of paint to have enough to cover the entire wall. 

 Jun 14, 2023
 #2
avatar+806 
0

 

Hello Monica.  Good work.  Excellent, even :-)   When I answered this same problem some time back, I took a slightly different path, but we both ended up at the same place, namely 104 gallons of paint.  I was happy to see someone else's answer was consistent with mine, because there was a "solution" even earlier than mine that ended with a different (read incorrect) answer.  Here's how I did it:    

 

 

You're going to have to convert those meters to square feet,  

so I think it's better to do it from the start.  Even though we'll  

have fractions to contend with, a calculator makes that easy.  

 

                                                                       12 m  

1 foot is 0.3048 meter, so the height is       –––––––––  =  39.3701 ft   

                                                                   0.3048 m/ft  

 

                                                                       120 m  

1 foot is 0.3048 meter, so the length is       –––––––––  =  393.7007 ft   

                                                                   0.3048 m/ft  

 

Area is height times length     (39.3701 ft)(393.7007 ft)  =  15,500.0359 sq ft  

 

1 gallon will cover 150 sq ft  

so divide that into the area               15,500.0359 sq ft  

                                                        –––––––––––––––  =  103.3335 gallons  

                                                           150 sq ft/gallon  

 

You can't buy just part of a gallon of paint,  

so we have to round that up to whole gallons                       104 gallons  

.

Bosco  Jun 14, 2023

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