A grocer wants to mix nuts which sell for Rs 40 per kilo with nuts which sell Rs 90 per kilo in order to make a mixture which could sell for Rs 70 per kilo.How many kilos of each should be mixed to get a mixture of 630 kilos?
A grocer wants to mix nuts which sell for Rs.14.40 per kilo with nuts selling for Rs.22.80 per kilo in order to make a mixture which would sell for Rs.18 per kilo.How many kilos of Rs.22.80 per kilo nuts should be mixed with 40 kilos of Rs.14.40 per kilo nuts?
To solve this problem, we can set up a system of equations.
Let's assume x represents the number of kilos of nuts that sell for Rs 40 per kilo, and y represents the number of kilos of nuts that sell for Rs 90 per kilo.
We are given the following information:
1) The price per kilo for the mixture should be Rs 70.
This can be represented by the equation:
(40x + 90y) / (x + y) = 70
2) The total weight of the mixture is 630 kilos.
This can be represented by the equation:
x + y = 630
Now, let's solve this system of equations.
We can start by rearranging the second equation to solve for x:
x = 630 - y
Substitute this value of x into the first equation:
[40(630 - y) + 90y] / (630 - y + y) = 70
Simplify the equation further:
[25200 - 40y + 90y] / 630 = 70
Combine like terms:
[25200 + 50y] / 630 = 70
Multiply both sides by 630:
25200 + 50y = 44100
Subtract 25200 from both sides:
50y = 18900
Divide both sides by 50:
y = 378
Now substitute the value of y back into the second equation to solve for x:
x + 378 = 630
Subtract 378 from both sides:
x = 252
Therefore, to get a mixture of 630 kilos, the grocer should mix 252 kilos of nuts that sell for Rs 40 per kilo with 378 kilos of nuts that sell for Rs 90 per kilo.
To solve this problem, we can set up a system of equations based on the given information. Let's assume the grocer needs to mix x kilos of nuts that sell for Rs 40 per kilo and y kilos of nuts that sell for Rs 90 per kilo to obtain a mixture of 630 kilos that sells for Rs 70 per kilo.
The first equation represents the total weight of the mixture:
x + y = 630
The second equation represents the total cost of the mixture:
(40x + 90y) / (x + y) = 70
Now, we can solve this system of equations to find the values of x and y.
First, let's rearrange the first equation to solve for x:
x = 630 - y
Next, substitute x in the second equation:
(40(630 - y) + 90y) / (630 - y + y) = 70
Simplify the equation:
(25200 - 40y + 90y) / 630 = 70
Combine like terms:
(50y + 25200) / 630 = 70
Now, cross multiply:
50y + 25200 = 70 * 630
Simplify:
50y + 25200 = 44100
Subtract 25200 from both sides:
50y = 44100 - 25200
50y = 18900
Divide both sides by 50:
y = 18900 / 50
y = 378
So, the grocer needs to mix 378 kilos of nuts that sell for Rs 90 per kilo.
To find the value of x, substitute y:
x = 630 - 378
x = 252
Therefore, the grocer needs to mix 252 kilos of nuts that sell for Rs 40 per kilo.
In summary, the grocer should mix 378 kilos of nuts that sell for Rs 90 per kilo and 252 kilos of nuts that sell for Rs 40 per kilo to obtain a mixture of 630 kilos that sells for Rs 70 per kilo.
amount used from the Rs 40 --- x
amount used from the Rs 90 --- 630-x
40x + 90(630-x) = 70(630)
40x + 56700 - 90x = 44100
-50x= -12600
x = 252
state conclusions.