1. Ratio Problem - Is My Answer Correct?

A fruit salad mixture consists of apples, peaches, and grapes in the ratio of 6:5:2, respectively, by weight. If 39 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?

What I did:
6+5+2= 13

39/13 (for the whole over the part) = 3

Then I multiplied 3 times each of the ratio numbers to get 18:15:6 and so the difference from the apples to grapes is 18-6 = 12. Is the answer 12 correct?

2. Originally Posted by thecapaccino
A fruit salad mixture consists of apples, peaches, and grapes in the ratio of 6:5:2, respectively, by weight. If 39 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?

What I did:
6+5+2= 13

39/13 (for the whole over the part) = 3

Then I multiplied 3 times each of the ratio numbers to get 18:15:6 and so the difference from the apples to grapes is 18-6 = 12. Is the answer 12 correct?
You are correct. but i think you did a bit too much work

so we have 6+5+2 = 13

so any weight will have the following proportions:
if the weight is w, then
6/13 * w = the weight of apples
5/13 * w = the weight of peaches
2/13 * w = the weight of grapes

in other words, we just put the ratio of each fruit over the sum of the ratios, and multiply whatever weight we get.

so for 39 pounds of fruit
the weight of apples is 6/13 * 39 = 18
the weight of grapes is 2/13 * 39 = 6

so there are 18 - 6 = 12 more pounds of apples than grapes.

there was no need to multiply the ratios by 3 to get 18:15:6, that step was done implicitly in what i did