Question 1207292: 360L of paint is made by mixing 3 paints A, B C . the ratio by amount of paint A to B is 3:2 and that of B to C is 1:2 Paint A costs 1800 per liter Paint B costs 2400 per liter and Paint C 1275 per litre . find the amount of each paint , the amount of money needed to make one liter of the mixture
Found 3 solutions by Theo, ikleyn, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a = number of liters of paint A.
b = number of liters of paint B.
c = number of liters of paint C.
you have a + b + c = 360.
a/b = 3/2.
cross multiply to get 2a = 3b
b/c = 1/2.
cross multiply to get 2b = c.
solve in terms of b for all ratios.
2a = 3b gets you a = 3b/2.
c = 2b gets you c = 2b.
a + b + c = 360 becomes 3b/2 + b + 2b = 360 after replacing a and c with their equivalent values in terms of b.
multiply both sides of that equation by 2 to get 3b + 2b + 4b = 720
combine like terms to get 9b = 720.
solve for b to get b = 720 / 9 = 80.
you have a = 3b/2 = 3*80/2 = 120.
b = 80.
c = 2b = 2*80 = 160.
a = 120, b = 80, c = 160.
a + b + c = 120 + 80 + 160 = 360.
A is 1800 per liter.
B is 2400 per liter.
C is 1275 per liter.
total price is 120 * 1800 + 80 * 2400 + 160 * 1275 = 612000.
612000 / 360 = 1700 per liter.
that's your solution.
1 liter of the mix would cost 1700.
Answer by ikleyn(52787)  (Show Source):
You can put this solution on YOUR website! .
360 liters of paint is made by mixing 3 paints A, B and C.
The ratio by amount of paint A to B is 3:2 and that of B to C is 1:2.
Paint A costs 1800 per liter. Paint B costs 2400 per liter. Paint C costs 1275 per liter .
(a) Find the amount of each paint in 360 liters of the mixture.
(b) Find the amount of money needed to make one liter of the mixture.
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To say that "The ratio by amount of paint A to B is 3:2 and that of B to C is 1:2" is the same
as to say that "The ratio by amount of paint A to B is 3:2 and that of C to B is 2:1".
Let 2x be the amount of paint B in 360 liters of the mixture.
Then the amount of paint A is  = 3x liters,
and the amount of paint C is 2*(2x) = 4x.
So, the 360 liters of the mixture is made of 3 equal parts of A,
two equal parts of B and 4 equal parts of C.
Or, in all, 360 liters of the mixture is made of 3+2+4 = 9 equal parts of A, B and C.
Thus each elementary part is 360/9 = 40 liters.
Hence, the 360 liters of the mixture paint is made of 3*40 = 120 L of paint A,
2*40 = 80 liters of paint B and 4*40 = 160 liters of paint C.
It completes question (a).
The total cost of 360 liters is then
120*1800 + 80*2400 + 160*1275 = 512000
and the cost of one liter of the mixture is
512000/360 = 1700.
It completes question (b).
Solved.
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I intently presented the solution at the level of arithmetic problem to avoid using equations,
since this logic and this reasoning is accessible to 4-th grade young students, who just know
addition, multiplication and division of integer numbers, but may not know equations yet.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The ratio of A to B is 3:2. A:B=3:2
The ratio of B to C is 1:2. B:C=1:2
Scale the second ratio up to make the same number for B in both ratios. B:C=2:4
Write a compound statement showing the ratios of all three. A:B:C=3:2:4
So paint A is 3/9 of the mixture, paint B is 2/9, and paint C is 4/9.
The mixture is 360L, so
A = (3/9)360 = 3*40 = 120L
B = (2/9)360 = 2*40 = 80L
C = (4/9)360 = 4*40 = 160L
We can use the fractions of the mixture that each paint is, along with the cost per liter of each paint, to find the cost of one liter of the mixture as a weighted average:
(3/9)(1800)+(2/9)(2400)+(4/9)(1275)=(5400+4800+5100)/9 = 15300/9 = 1700
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