题目信息
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?(4 quarts = 1 gallon)
A:$54
B:$60
C:$66
D:$90
E:$144
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正确答案：
C:$66
Arithmetic Applied problems
To make 3 gallons of the mixture requires 12 quarts, and the least amount of money is achieved by purchasing the greatest number of gallons and least number of quarts. Letting B be the number of quarts of blue paint needed and W be the number of quarts of white paint needed, it follows that B + W = 12, where B =
since the mixture has a blue to white ratio of 3 to 2. This gives B = 
and W = 
. Since the paint can be purchased in whole quarts only, the painter must purchase 8 quarts or 2 gallons of blue, and 5 quarts or 1 gallon plus 1 quart of white for a total of (2 + 1)($18) + $12 = $66.
The correct answer is C.
To make 3 gallons of the mixture requires 12 quarts, and the least amount of money is achieved by purchasing the greatest number of gallons and least number of quarts. Letting B be the number of quarts of blue paint needed and W be the number of quarts of white paint needed, it follows that B + W = 12, where B =
since the mixture has a blue to white ratio of 3 to 2. This gives B = and W = . Since the paint can be purchased in whole quarts only, the painter must purchase 8 quarts or 2 gallons of blue, and 5 quarts or 1 gallon plus 1 quart of white for a total of (2 + 1)($18) + $12 = $66.The correct answer is C.
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