A farmer has enough space in his farm to rear 200 birds. He buys chickens at $1 each and ducklings at $2 each. He cannot spend more than $250 for purchasing the birds. What are the possible numbers of birds he can purchase?

Solution:

Here’s how you solve this type of question:

1. Assume that the maximum number of birds he can purchase’s 200, since he does not have space for more than that. Of course, he could purchase more and then release them into the wild, but we don’t think that’s what your teacher has in mind!
2. One option is to buy no birds at all, and keep the $250.
3. Since chickens cost only $1 each, he could buy 200 chickens and have $50 left over.
4. Or he could buy 125 ducklings and have no money left over.
5. So there are lots of possibilities. The general formula would be given by c + 2d 250 and c + d  200, where c is the number of chickens and d is the number of ducklings. Since we are dealing with a real world situation, we can also assume that c and d are non-negative integers. The solution space would look like this:

The above chart shows all the possible numbers of chickens and ducklings that would satisfy the constraints of space and money. As you can see, there are thousands of options.

This entry was posted on Thursday, July 22nd, 2010 at 8:18 am and is filed under 10th Grade, Homework Answers, Math Answers. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.