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?	Select the correct option
A) 15
B) 10
C) 9
D) 6
E) 4

Rationale: "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 = 12 x : 8 x : 7 x 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 : 12 x + 8 x + 7 x = 54 27 x = 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 = 10 more pounds of apples than grapes . answer is b ."
Answer: B