# A grocery store offers a cheese sampler that includes a pepper cheddar cheese that costs $15 per kilogram and Pennsylvania Jack

###### Question:

## Answers

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

[tex]x=\frac{7.5}{5}[/tex]

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