Question 1189865
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A certain brand of house paint must be purchased either in quarts at $12 each or in gallons at $18 each. 
A painter needs a 3-gallon mixture of the paint consisting of 3 parts blue and 2 parts white. 
What is the least amount of money needed to purchase sufficient quantities of the two colors 
to make the mixture?
a)$54 b)$60 c)$66 d)$90 e)$144
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            This problem is to apply common sense and a bit of arithmetic and simple algebra.



<pre>
To start, notice that

    1 gallon = 4 quarts,  and

    buying in gallons is much cheaper than buying the same amount in quarts, both for blue and for white paint.



The parts of the 3-gallon mixture are 1.8 gallons of blue paint and 1.2 gallons of white paint 

    (easy calculate with algebra  3x + 2x = 3 gallons;  5x = 3 gallons;  x = 0.6 of a gallon;  and the parts are 3x and 2x).


    +---------------------------------------------------------------------------------+
    |        So, we can solve the problem (minimize the cost) separately              |
    |    for 1.8 gallons of the blue paint and for 1.2 gallons of the white paint.    |
    +---------------------------------------------------------------------------------+


1.8 gallons of the blue paint is the same as 1 gallon and 3.2 quarts,

so for 1.8 gallons of the blue paint we have two options:

    to buy 1 gallon plus 4 quarts separately,  which costs  18 + 4*12 = 66 dollars,

    or to buy 2 gallons (which is enough),  which costs  2*18 = 36 dollars.


The choice is clear, and we buy 2 gallons of the blue paint, paying 36 dollars.



1.2 gallons of the white paint is the same as 1 gallon and 0.8 quarts,

so for 1.2 gallons of the white paint we have two options:

    to buy 1 gallon plus 1 quarts,  which costs  18 + 12 = 30 dollars,

    or to buy 2 gallons (which is enough),  which costs  2*18 = 36 dollars.


The choice is clear, and we buy 1 gallon plus 1 quart of the white paint, paying 30 dollars.



In total, the optimal purchase costs  36 + 30 = 66 dollars.     <U>ANSWER</U>
</pre>

Solved.