Math word probelm

Question

a party mix is made by adding nuts that sell for 2.50 per kg to a ceral mixture that sells for 1 kg how much of each should be added to obtain 30kg of a mix that will sell for 1.70 per kg? 

Answer 1

Marie, I am assuming that the cereal mixture sells for 1.00 per kg. If that is the case, then let:

 

x = the amount of nuts

y = the amount of cereal

 

Then we know since the party mix is 30 kg that:

 

x + y = 30

 

We also know that:

 

2.50x + 1.00y = 30 (1.70)   Let's multiply thru by 100

250x + 100y = 30(170)

250x + 100y = 5100

 

Let's now solve x + y = 30 for y.

 

y = 30 - x

 

We can substitute this into the other equation.

 

250x + 100(30 - x) = 5100

250x + 3000 - 100x = 5100

150x + 3000 = 5100

150x = 2100

x = 14

 

So y = 30 - 14 = 16

 

There should be 14 kg of nuts and 16 kg of cereal mix