SOLUTION: A grocery store offers a cheese sampler that includes a pepper cheddar cheese that costs $13 per kilogram and Pennsylvania Jack that costs $9 per kilogram. How many kilograms of ea

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Question 1200089: A grocery store offers a cheese sampler that includes a pepper cheddar cheese that costs $13 per kilogram and Pennsylvania Jack that costs $9 per kilogram. How many kilograms of each were used to make a 5-kilogram mixture that costs $10.20 per kilogram?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Routine, been done many times in different examples.

pepper cheddar $13 per kg
penn jack $9 per kg
want mix of 5 kg costing $10.2 per kilogram

If use unknown w kg of pepper cheddar then 13w%2B9%285-w%29=%2810.2%29%285%29; and you can simplify and solve for w. Hold off on all computations until last.

Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
.
A grocery store offers a cheese sampler that includes a pepper cheddar cheese
that costs $13 per kilogram and Pennsylvania Jack that costs $9 per kilogram.
How many kilograms of each were used to make a 5-kilogram mixture that costs $10.20 per kilogram?
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x kilos per $13 and (5-x) kilos per $9.


Your money equation is

    13x + 9*(5-x) = 5*10.20  dollars.


Simplify and find x

    13x + 45 - 9x = 51.00

    13x - 9x = 51 - 45

        4x   =    6

         x   =    6/4 = 1.5 kilograms.


ANSWER.  1.5 kilograms per $13 and (5-1.5) = 3.5 kilograms per $9.


CHECK.  %281.5%2A13+%2B+3.5%2A9%29%2F5 = 10.20 dollars per kilogram.   ! correct !

Solved.

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It is a very advanced grocery store, measuring their production in kilograms (!)



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


If you don't need a formal algebraic solution, and if getting to the answer quickly is important (as in a timed math competition), then here is a way to solve any 2-part "mixture" problem like this.

$10.20 is 1.20/4.00 = 3/10 of the way from $9.00 to $13.00
That means 3/10 of the mixture should be the more expensive cheese

ANSWER: 3/10 of 5 kg, or 1.5 kg, of the more expensive pepper cheddar cheese; the other 3.5 kg of the less expensive Pennsylvania Jack.