Question

A grocery store offers a cheese sampler that includes a pepper cheddar cheese that costs $12 per kilogram and Pennsylvania Jack that costs $11 per kilogram. How many kilograms of each were used to make a 5-kilogram mixture that costs $11.30 per kilogram?

Answer 1

3.5 kg of Pennsylvania Jack and 1.5 kg of Cheddar

Explanation:

Let C be the kg of cheddar cheese and P be the kg of Pennsylvania Jack cheese needed for the sampler.

We know that C is $12/kg and P is $11/kg.

We can say that the total cost for a cheese sampler would be:

12C + 11P = Total Cost

We need to find a 5 kg mixture:

C + P = 5 kg

that costs $ll.30/kg. The total cost would be: (5kg)($11.30/kg) = $56.50

C + P = 5 kg

Rearrange C + P = 5 kg to:

C = 5kg - P and then use this in the cost equation:

12C + 11P = $56.50

12(5 - P) + 11P = 56.50

60 - 12P + 11P = 56.50

-P = - 3.50

P = 3.50 kg

That means we have:

C + P = 5 kg

C + 3.50 = 5 kg

C = 1.50 kg

Check to see if these values work:

12C + 11P = $56.50

12(1.50) + 11(3.50) = 56.50?

18.00 + 38.50 = 56.50 YES