a health food store sells a mixture. raisins sell for 3.50/kg and nuts will sell for 4.75/kg. how many kilograms of each should be mixed to make 20kgworth$4/kg

Question

Please have answer by 2:00pm

Answer 1

Let r be the amount of raisins and let n be the amount of nuts.

 

So you know that you want a total of 20 kg, so that gives you the first equation:

 

r + n = 20

 

You also know that you want the average price to be $4 per kg.  Since the total is going to be 20 kg, that means that the total value of the 20 kg will be $80.

 

Since the raisins are $3.50 per kg, the value of the raisins in the mixture will be 3.5 r

 

And similarly, the value of the nuts will be 4.75 n

 

So the total value will be 3.5 r + 4.75 n, and that has to add up to 80.  That gives you the second equation:

 

3.5 r + 4.75 n = 80

 

So let's solve these together. 

 

r + n = 20

3.5 r + 4.75 n = 80

 

Start by multiplying both sides of the first equation by 3.5:

 

3.5 r + 3.5 n = 3.5 * 20 = 70

3.5 r + 4.75 n = 80

 

Subtract the first equation from the second:

1.25 n = 10

 

So n = 8

 

And since n + r = 20, that means that r = 12.

 

So there should be 8 kg of nuts and 12 kg of raisins.