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Question 1101803: a trader deals in two types of rice, type A and type B . type A costs ksh.400.00 per bag and type B costs ksh.350.00 per bag.
a) the trader mixes 30 bags of type A With 50 bags of type B. if he sells the mixture at a profit of 20% , calculate the selling price of one bag of the mixture.
b)the trader now mixes type A with type B in the ratio x : y respectively. if the cost of the mixture is ksh.383.50 per bag, find the ratio X : Y ?
C)the trader mixes one bag of the mixture in part (a) with one bag of the mixture in part (b) above . calculate the ratio of type A rice to type B rice in this mixture?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x equal the number of bags of type A and let y = the number of bags of type B.
the total number of bags of the mixture would be x + y.
the average price of the mixture per bag would be the total cost of the mixture divided by the total number of bags.
if the cost per bag of type A is 400 and the cost per bag of type B is 350, then the total cost of the mixture would be 400 * x + 350 * y = m * (x + y).
m is the cost per bag of the mixture.
if you want to find the cost per bag of the mixture, then you would divide both sides of the equation by (x + y)
you would get m = (400 * x + 350 * y) / (x + y)
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a) the trader mixes 30 bags of type A With 50 bags of type B. if he sells the mixture at a profit of 20% , calculate the selling price of one bag of the mixture.
you are given that x = 30 pounds and y = 50 pounds.
400 * x + 350 * y = m * (x + y) becomes:
400 * 30 + 350 * 50 = m * (30 + 50).
the cost per bag of the mixture becomes m = (400 * 30 + 350 * 50) / (30 + 50)
solve for m to get m = 368.75 per bag.
the selling price of the mixture assuming a 20% profit would be 368.75 * 1.2 = 442.5 per bag.
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b)the trader now mixes type A with type B in the ratio of x : y respectively. if the cost of the mixture is ksh.383.50 per bag, find the ratio x:y.
the ratio of the number of bags of type A to the number of bags of type B is equal to x/y.
the total number of bags in the mixture is therefore x + y.
the cost formula becomes 400 * x + 350 * y = m * (x + y)
you are given that m = 383.5.
the formula becomes 400 * x + 350 * y = 383.5 * (x + y)
simplify this to get 400 * x + 350 * y = 383.5 * x + 383.5 * y
subtract 383.5 * x from both sides of the equation and subtract 350 * y from both sides of the equation to get:
400 * x - 383.5 * x = 383.5 * y - 350 * y
simplify to get 16.5 * x = 33.5 * y
divide both sides of the equation by y and divide both sides of the equation by 16.5 to get:
x/y = 33.5/16.5
that's the ratio of x to y.
it can also be expressed as x/y = 67/33 if you need integers in the numerator and denominator.
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C)the trader mixes one bag of the mixture in part (a) with one bag of the mixture in part (b) above. calculate the ratio of type A rice to type B rice in this mixture?
one bag of mixture in part A contains 30/80 bags of type A and 50/80 bags of type B.
one bag of mixture in part B contains 33.5/50 bags of type A and 16.5/50 bags of type B.
the total bags of type A in the new mixture = 30/80 + 33.5/50 = 150/400 + 268/400 = 418/400 = 209/200 bags.
the total bags of type B in the new mixture = 50/80 + 16.5/50 = 250/400 + 132/400 = 382/400 = 191/200 bags.
the ratio of type A bags to type B bags in the new mixture is therefore 209 / 191.
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