Question

A grocery store offers a cheese sampler that includes a pepper cheddar cheese that costs $18 per kilogram and Pennsylvania Jack that costs $12 per kilogram. How many kilograms of each were used to make a 6-kilogram mixture that costs $14.50 per kilogram?

Answer 1

Let x be the number of kilograms of pepper cheddar cheese and y be the number of kilograms of Pennsylvania Jack cheese.

We are given that the total weight of the mixture is 6 kilograms, so we have:

`x + y = 6`

We are also given that the cost of the mixture is $14.50 per kilogram, so we have:

`18x + 12y = 14.5(6)`

Simplifying the second equation:

`18x + 12y = 87`

Dividing both sides by 6 to simplify:

`3x + 2y = (29)/(2)`

Now we have two equations with two variables:

`x + y = 6 \\ 3x + 2y = (29)/(2)`

We can solve for x in the first equation:

`x = 6 - y`

Substituting this expression for x into the second equation:

`3(6 - y) + 2y = (29)/(2)`

Simplifying and solving for y:

`18 - 3y + 2y = (29)/(2)\\-y = -(5)/(2)\\y = (5)/(2)`

Now that we know y is 5/2, we can find x:

`x = 6 - y \\ x = 6 - (5)/(2) \\ x = (7)/(2)`

Therefore, we need 7/2 kilograms of pepper cheddar cheese and 5/2 kilograms of Pennsylvania Jack cheese to make a 6-kilogram mixture that costs $14.50 per kilogram.

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`\large\qquad\qquad\qquad\rm 06/21/2023`