|
||||||||||||
|
||||||||||||
![]() |
||||||||||||
| ||||||||||||
![]() | ||||||||||||
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 re-write 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 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, | ||||||||||||
|
||||||||||||
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. |