Question

A grocery store offers a cheese sampler that includes a pepper cheddar cheese that costs $15 per kilogram and Pennsylvania Jack that costs $8 per kilogram. How many kilograms of each were used to make a 7-kilogram mixture that costs $10.50 per kilogram?

Answer 1

Answer: The quantity of pepper cheddar cheese required = 2.5 kilograms

The quantity of Pennsylvania Jack required = 4.5 kilograms

Step-by-step explanation:

Let x = Quantity of pepper cheddar cheese

y=  Quantity of Pennsylvania Jack

As per given , we have the following system of equations:

$x+y=7----------(1)\\\\ 15x+8y= 7\times10.50\\\\ 15x+8y=73.5------------(2)$

Multiply 8 to equation(1) , we get

$8x+8y=56---------(3)$

Eliminate (3) from (2) , we get

$7x=17.5\\\\ x=\dfrac{17.5}{7}=2.5$

Put value of x in (1) , we get

$2.5+y=7\\\\ y=7-2.5=4.5$

Hence, the quantity of pepper cheddar cheese required = 2.5 kilograms

The quantity of Pennsylvania Jack required = 4.5 kilograms