



 
Hi Robby. This is a kind of hard problem for 7th grade  good for you for trying to figure it out! Let's start with some algebra: Then m + w + c = 100, because there are 100 people in all. Also, 3m + 2w + (1/2)c = 100, because we want the 100 bushels to divide evenly according to the proportions given. We can rewrite these both. The first one can be written like this:
and the second can be written:
Double the last line and you get:
Notice that we have two equations ending in "= c". Now, remember that two things that both equal a third thing have to equal each other, so that means:
and this simplifies to
There is a lot of information in this equation. First of all the right side is divisible by 5 so the left side is divisible by 5. Since 3 is not divisible by 5, w must be divisible by 5. Hence the only possibilities for w are 0, 5, 10, ..., 100. But w certainly can't be 100 since 3 w would be 300. So how large can w be? If w = 35 then 3 w = 105 which is too large so w can only be 0, 5, 10, 15, 20, 25 or 30. That's only 7 cases so you can try them all. For each possible w find m using 3w = 100  5m and then c using m + w + c = 100 and check to see if Hope this helps,  


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