|
Question 1101893: akinyi bought maize and beans from a wholesaler . she then mixed the maize and beans in the ratio 4 : 3, she bought the maize at ksh.21.00 per kilogram and the beans at ksh.42.00 per kilogram. if she was to make a profit of 30% . what should be the selling price of 1 kg of the mixture?
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! Cost for 1 kilogram of the mixture, 30 ksh.
If wanting 30% profit, then selling price should be  ksh per kilogram.
PRICE Qty COST
Maize 21 4x 21*4x
Beans 42 3x 42*3x
Total 7x 210x
Mixture cost for 7x kilograms is 210x ksh;
price of the mixture before adjustment for making profit,  .
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the maize and beans were mixed in a 4 to 3 ratio by weight.
that means 4 kilograms of maize for every 3 kilograms of beans.
that means that, for every 7 kilograms of mixture, 4 kilograms is maize and 3 kilograms is beans.
if you let x equal the number of kilograms in the mixture, then you get:
4 * x + 3 * x = 7 * x
divide both sides of that equation and you get:
4/7 * x + 3/7 * x = x
x represents the total weight of the mixture.
4/7 * x represents the the weight of the maize in the mixture.
3/7 * x represents the weight of the beans in the mixture.
the cost of the maize is equal to 21 ksh per kilogram.
the cost of the beans is equal to 42 ksh per kilogram.
the cost of the maize in the mixture is therefore equal to 4/7 * x * 21 = 12 * x.
the cost of the beans in the mixture is therefore equal to 3/7 * x * 42 = 18 * x.
the total cost of the mixture is therefore equal to 12 * x + 18 * x which is equal to 30 * x.
the profit needs to be 30% of the cost, therefore the profit is equal to .3 * 30 * x which is equal to 9 * x.
you have:
total cost is 30 * x
profit is equal to 9 * x.
akinyi needs to charge the customer 30 * x + 9 * x = 39 * x ksh.
since x represents the weight of the mixture in kilograms, and you want to know how much akinyi needs to charge for the mixture to make 30% profit, then she needs to charge 39 * 1 = 39 ksh.
that's the selling price of the mixture.
she sells 1 kilogram for 39 ksh.
39 ksh represents 1.3 * the cost.
to find the cost, divide 39 by 1.3 to get a cost of 30 ksh.
her profit is 39 - 30 = 9 ksh.
9 ksh is equal to 30% of 30 ksh.
this formula works for any number of kilograms of mixture.
if she sold 10 kilograms of the mixture, then she needs to charge 39 * 10 = 390 ksh.
390 ksh represent 1.3 * the cost.
divide that by 1.3 and you get 390 / 1.3 = 300 ksh which represents the cost.
her profit is 390 - 300 = 90 ksh.
90 ksh is 30% of 300 ksh.
to summarize:
the ratio by weight of maize to beans in the mixture is 4/3.
let x = the weight of the mixture and you get:
the weight of the maize in the mixture is 4/7 * x.
the weight of the beans in the mixture is 3/7 * x.
the cost of the maize in the mixture is 4/7 * x * 21 = 12 * x.
the cost of the beans in the mixture is 3/7 * x * 42 = 18 * x.
the total cost of the mixture is 12 * x + 18 * x = 30 * x.
at 30% profit, the price to the customer has to be 30 * x * 1.3 = 39 * x.
if she sells 1 kilogram of the mixture, then x = 1 and the price to the customer has to be 39 ksh.
the selling price is 39 ksh.
|
|
|
| |
