A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 12:8:7, respectively, by weight. If 54 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?  Choose the correct choice from the following options
A) 15	B) 10	C) 9	D) 6	E) 4
We can first set up our ratio using variable multipliers. We are given that a fruit-salad mixture consists of apples, peaches, and grapes, in the ratio of 6:5:2, respectively, by weight. Thus, we can say:   apples : peaches : grapes = 12x : 8x : 7x   We are given that 54 pounds of the mixture is prepared so we can set up the following question and determine a value for x:   12x + 8x + 7x = 54   27x = 54   x = 2   Now we can determine the number of pounds of apples and of grapes.   pounds of grapes = (7)(2) = 14   pounds of apples = (12)(2) = 24   Thus we know that there are  24-14= 
<gadget id="calculator"> 24-14</gadget>
<output>10</output>
10 more pounds of apples than grapes.   Answer is 10.
<result>B</result>
A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 12:8:7, respectively, by weight. If 54 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?