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Question 764357: A stadium is painted gold, blue and red in the ratio 5:4:2. It is estimated that the stadium has a paintable area of 445.5m2. If 1 litre of paint covers 15m2, find the amount required of each paint colour. (in whole litres)
I have tried to work this problem out using fractions, but it has gotten me confused at the part where it has the paintable area and how much 1 litre of paint covers. I'm not sure where they fit in the equation.
Thanks
Found 2 solutions by ramkikk66, DrBeeee:
Answer by ramkikk66(644)   (Show Source):
You can put this solution on YOUR website!
Your question:
A stadium is painted gold, blue and red in the ratio 5:4:2. It is estimated that the stadium has a paintable area of 445.5m2. If 1 litre of paint covers 15m2, find the amount required of each paint colour. (in whole litres)
Solution:
1) First we find out what is the area to be covered by each colour. The ratio of
5:4:2 means that for every 5 parts of gold, you use 4 parts of blue and 2 parts
of red. So in a total of (11) parts, gold is 5, blue = 4 and red = 2.
2) So gold forms 5/11 of the area, blue covers 4/11 and red covers 2/11.
3) Since total area is 445.5,
Area covered by gold = 445.5*5/11 = 202.5 m^2
Area covered by blue = 445.5*4/11 = 162.0 m^2
Area covered by red = 445.5*2/11 = 81.0 m^2
(Quick check: 202.5 + 162 + 81 should total up to 445.5, which it does)
4) Now since you need 1 liter of paint for 15 m^2 it is easy to find how many
liters you need for each colour.
Liters of gold paint = 202.5/15 = 13.5 liters
Liters of blue paint = 162.0/15 = 10.8 liters
Liters of red paint = 81.0/15 = 5.4 liters
:)
Answer by DrBeeee(684) (Show Source):
You can put this solution on YOUR website! If one liter covers 15m^2, there is no way to get whole liters to cover 445.5m^2. The ratio is 29.7L. So let's forget that so called requirement.
This is a problem in which we use the Nicole "n". So called after one of my students, Nicole.
We simply start with the ratio 5:4:2 and multiply each ratio by a constant "n" and get
(1) 5*n:4*n:2*n, wherein the ratios have not changed because n is a constant.
Now we can add the number of liters of the three colors and equate it to the total amount of paint required or
(2) 5*n + 4*n + 2*n = 445.5/15 or
(3) 11*n = 29.7 or
(4) n = 29.7/11 or
(5) n = 2.7
For each color we need the following number of liters;
a) Gold = 5*n or 5*2.7 or 13.5L
b) Blue = 4*n or 4*2.7 or 10.8L
c) Red = 2*n or 2*2.7 or 5.4L
Add them up and get 29.7L, which will cover 15*29.7 or 445,5m^2
Answer is given by a, b, and c above.
Note that the ratio 13.5:10.8:5.4 is the same as 5:4:2, thanks to Nicole!
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