This ratio tells you that for every 9 grapes, there are 3 walnuts and 11 oranges. The purpose of a ratio is to tell you how much of something you have with respect to other objects, in the simplest numbers possible.
So from this information, if I said I have 6 walnuts, I would know that there are 18 grapes and 22 oranges on hand. If I have double the amount of walnuts, I would have to have double the amount of everything else.
Onto the question at hand, this question is telling us that we have 161 fruits. As you can see, this is a trick question, because a walnut is not a fruit, so we can just ignore it for now. So what the ratio is telling us, is that for every 9 grapes, we have 11 oranges. It is also telling us that for every 9 grapes, or for every 11 oranges, we have 20 total fruits.
The ratio of grapes to fruits is therefore 9:20. If you want to think about it in fractional form, its 9/20. 9 twentieths of the total fruit are grapes. Now that we are thinking about this in terms of fractions, we can jus go ahead and solve the problem. If we have 161 fruits, and 9 out of 20 of those fruits are grapes, how many grapes are there?
The answer is 72.45 grapes. Im not very happy with this answer because it is not a whole number, and you would think the author of the question wouldn't want to have an answer where theres just a half eaten grape laying on your fruit tray. I believe this is a trick question a typo because if you were not to remove the walnuts from the ratio, making it 9 grapes for every 23 objects, the numbers suddenly work out with all whole numbers (63 grapes). You might want to ask your teacher if there was a mistake, because 63 is a much more appealing number and it doesnt make much sense to have decimal places when you are working with discrete objects like pieces of fruit.
3/28/2013

Justin M.