Question 1149894: A paint dealer mixes three types of paint A, B and C in the ratios A:B = 3:4 and B:C = 1:2. the mixture is to contain 168 litres of C . A)find the ratio A:B:C
B) Find the required number of litres of B
C)The cost per litre of type A is sh.160, type B is sh.205 and type c is sh.100 . i) calculate the cost per liter of the mixture
ii) find the percentage profit if the selling price of the mixture is sh.182 per liter. iii) find the selling price of a liter of the mixture if the dealer makes a 25% (profit?).
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the ratios are:
A:B = 3:4
this ratio says that, for every 3 parts of A, you have 4 parts of B.
B:C = 1:2
this ratio says that, for every 1 part of B, you have 2 parts of C.
to combine these 2 ratios into 1 overall ratio, you need 4 parts of B.
the corresponding ratio of B:C would be B:C = 4:8.
the overall ratio becomes A:B:C = 3:4:8
this ratio says that for every 3 parts of A, you have 4 parts of B and for every 4 parts of B, you have 8 parts of C.
if the mixture contains 168 liters of C, divided that by 8 and multiply it by 4 to get 84 liters of B. divide that by 4 and multiply it by 3 to get 63 liters of A.
you have 63 liters of A and 84 liters of B and 168 liters of C.
the ratio of A:B is 3:4.
A:B = 3:4 can be written as A/B = 3/4.
solve for B to get B = 4/3 * A.
this makes B = 4/3 * 63 = 84.
the ratio of B:C is 1:2.
this can be written as B/C 1/2.
solve for C to get C = 2 * B
this makes C = 2 * 84 = 168
note that A:B = 3:4 can also be written as A/B = 3/4.
note that B:C = 1:2 can also be written as B/C = 1/2.
not also that B/C = 1/2 is equivalent to B/C = 4/8 which can also be written as B:C = 4:8.
you have A:B = 3:4 and B:C = 4:8 which can then be written as A:B:C = 3:4:8.
we have:
A = 63
B = 84
C = 168
the cost per liter of type A is 160.
the cost per liter of type B is 205.
the cost per liter of type C is 100.
assuming 168 liters of type C, then the overall cost of the mixture would be:
160 * 63 + 205 * 84 + 100 * 168 = 44100.
divide that by the total liters of 63 + 84 + 168 = 315 and the overall cost per liter of the mixture is 44100 / 315 = 140.
if the selling price of the mixture is 182, then the percent profit = (182-140)/140 * 100 = 30%.
if the dealer wants to make a 25% profit, then the equation for that is 25% = (x - 140) / 140 * 100.
divide both sides of this formula by 100 to get:
.25 = (x - 140) / 140
multiply both sides of this formula by 140 to get:
35 = x - 140
solve for x to get x = 175.
the dealer would have to make the selling price equal to 175 so that the dealer can make a 25% profit.
(175 - 140) / 140 * 100 = 25%.
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