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:
[tex]x+y=7----------(1)\\\\ 15x+8y= 7\times10.50\\\\ 15x+8y=73.5------------(2)[/tex]
Multiply 8 to equation(1) , we get
[tex]8x+8y=56---------(3)[/tex]
Eliminate (3) from (2) , we get
[tex]7x=17.5\\\\ x=\dfrac{17.5}{7}=2.5[/tex]
Put value of x in (1) , we get
[tex]2.5+y=7\\\\ y=7-2.5=4.5[/tex]
Hence, the quantity of pepper cheddar cheese required = 2.5 kilograms
The quantity of Pennsylvania Jack required = 4.5 kilograms
2.5 kg of pepper cheddar cheese and 4.5 kg of Pennsylvania Jack was used to make the mixture.
Let x represent the pepper cheddar cheese and y represent the Pennsylvania Jack.
To make a 7 kg mixture:
x + y = 7 (1)
The mixture cost $10.50 per kilogram:
15x + 8y = 10.5(7)
15x + 8y = 73.5 (2)
Solving equation 1 and 2 simultaneously gives:
x=2.5, y = 4.5
Hence 2.5 kg of pepper cheddar cheese and 4.5 kg of Pennsylvania Jack was used to make the mixture.
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