SOLUTION: A grocery store offers a cheese sampler that includes a pepper cheddar cheese that costs $18 per kilogram and Pennsylvania Jack that costs $8 per kilogram. How many kilograms of ea

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Question 1182418: A grocery store offers a cheese sampler that includes a pepper cheddar cheese that costs $18 per kilogram and Pennsylvania Jack that costs $8 per kilogram. How many kilograms of each were used to make a 5-kilogram mixture that costs $11.00 per kilogram?
pepper cheddar
kg
Pennsylvania Jack
kg
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x of pepper cheddar
y of pennsylv jack
system%28x%2By=5%2C18x%2B8y=11%2A5%29

Use y in terms of x.
y=5-x

highlight_green%2818x%2B8%285-x%29=55%29-------solve this for x, and then find the value for y (or just evaluate 5-x).

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The conditions of the problem make for an easy setup of the problem using two variables for the numbers of kilograms of the two kinds of cheese:

x = kg of pepper cheddar
y = kg of Pennsylvania Jack

x+y=5 the total number of kilograms is 5
18x+8y=55 the total cost of the mixture is $55 (5 kg at $11 per pound)

Given those two equations, the solution from the other tutor uses substitution to solve the problem.

That is a valid method -- but when the two equations are both in Ax+By=C form, I think elimination is much easier.

8x+8y=40 (1st equation, multiplied by 8)
18x+8y=55
10x=15 (difference between the two equations, eliminating y)
x=1.5

ANSWER: x=1.5 pounds of pepper cheddar; the other 3.5 pounds of Pennsylvania Jack

And here is a very quick and easy non-algebraic method for solving this or any other 2-part mixture problem.

Look at the three prices on a number line -- 8, 11, and 18 -- and observe/determine/calculate that 11 is 3/10 of the way from 8 to 18.

That means 3/10 of the mixture is the more expensive cheese.

ANSWER: 3/10 of 5 kg, or 1.5 kg, of the pepper cheddar and the other 3.5 kg of Pennsylvania Jack.