A certain brand of house paint must be purchased either in quarts at $12 each or

游客2025-02-27 11

问题 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)

选项 A、$54
B、$60
C、$66
D、$90
E、$144

答案 C

解析 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 = 3W/2 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 + l)($18) + $12 = $66.
The correct answer is C.

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