Posted by **Reiny** on Wednesday, September 16, 2009 at 8:45am.

"100 bushels of corn are divided among 100 men, women, and children. Men receive 3 bushels each, women 2 bushels and children 1/2 bushel each. How can the bushels be distributed? is there more than one solution? if so, find the other solutions."

let the number of men be x

the number of women be y

and the number of children be (100-x-y)

then 3x + 2y + (1/2)(100-x-y) = 100

6x + 4y + 100 - x - y = 200

5x + 3y = 100

this is a linear relations where one obvious solution is (20,0)

the 'slope' is -5/3, that is,

for every decrease of 3 in the x's we can increase y by 5 and we have another solution.

so other solutions are

(17,5)

(14,10)

(11,15) etc.

of course we have to check if the number of children is still valid.

e.g. for (11,15)

we would have 11 men, 15 women and 100-11-15 or 74 children

check: 11(3) + 15(2) + (1/2)(74) = 100 YEAH!

keep my pattern going for the rest of the results.

## Answer this Question

## Related Questions

- MATH - 100 bushels of corn are divided among 100 men, women, and children. Men ...
- economics - Suppose that there are two states that do not trade: Iowa and ...
- Mircoeconomics - Figure 3-1 ____ 2. Refer to Figure 3-1. Assume that Cliff and ...
- Algebra - An apple orchard charges a fixed amount for the first four bushels of ...
- Math - Mr. Farmer plans to harvest 305% of what he sows. How many bushels of ...
- Economics: Comperative Advantage - Refer to Figure 4. Assume that Cliff and Paul...
- economics - Assume Cliff and Paul were both producing wheat and corn, and each ...
- environmental science - A farmer planted a fiel od BT-123 corn and wants to ...
- science - A farmer planted a field of Bt 123 corn and wants to estimate the ...
- Math - A farmer planted a field of Bt 123 corn and wants to estimate the yield ...

More Related Questions