A grocery store offers a cheese sampler that includes a pepper cheddar cheese that costs $15 per kilogram and Pennsylvania Jack that costs $10 per kilogram. How many kilograms of each were used to make a 6-kilogram mixture that costs $11.25 per kilogram?

1.5 kg of  pepper cheddar cheese; and

4.5 kg of  Pennsylvania Jack

Step-by-step explanation:

Given that;

the amount of the mixture formed = 6 kg

Then if (x) is the amount of pepper cheddar cheese in the mixture

then the  amount of Pennsylvania Jack  in the mixture = 6 - x

Let apply the value mixture equation V = AC

where;

V= value of the ingredient

A = amount of the ingredient

C = unit cost of the ingredient

From, the data given in the question; we have

                 Amount (A)                  Unit cost (C)           = Value (V)

Pepper

Cheddar           x                                 15                       = 15x

Cheese

Pennsyl-

vania              6-  x                              10                       = 10(60-x)

Jack

Mixture           6                                   11.25                   = 67.50

The sum of the values of the two ingredient must definitely be equal to the value of the mixture; as such

15x + 10(6-x) = 67.5

15x + 60 - 10x = 67.5

5x + 60 = 67.5

5x = 67.5 -60

5x = 7.5

x = 1.5

From 6 -x =0

we have 6 -1.5  = 0

= 4.5

Hence, 1.5 kg of pepper cheddar cheese that costs $15 per kg should be mixed with 4.5 kg of Pennsylvania Jack that costs $ 10 per kg