| Original Problem: | Marge bought 5 dozen baby trees to plant around her house. Oak trees cost $5 each, elm trees cost $3 each, and yew trees cost $0.50 each. If Marge spent exactly $100, how many of each kind of baby tree did she buy? |
1. Problem Statement
This problem is called Baby Trees. Baby elms cost $3, oak trees cost $5, and yew trees cost $0.50. You need to find out how many of each tree you need to equal $100 if there are 60 trees all together.
2. Process
First I figured out the total number of trees Marge bought. Five dozen is
5 x 12 = 60. My first idea was that she got the same number of each kind of tree. So I divided 60 by 3 and got 20 trees of each kind. I multiplied 20 times the price of each kind of tree.
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The total price for these 60 trees was $170 (20 x $5 is already $100) which was too high. So that wasn't be right.
Next I tried the guess and check method with a few numbers. I tried 2 oaks and many different combinations of elms and yews and then I tried 7 oaks and more combinations. Even though I tried a lot, I still couldn't find the solution.
Then I decided to try and solve an easier problem and see if I could use the answer to the easy one to figure out the real answer. I started by reducing $100 for 60 trees down to $10 for 6 trees. That way, if I could find a way to solve this problem, I could take that answer and multiply it by 10 to get the final solution.
Obviously, if 6 trees cost $10, there could only be one oak tree since oaks cost $5 each. Buying one oak leaves $5 to spend on five more trees. Now with $5 I could buy only one elm tree. That left me with $2 to buy 4 trees. But that is exactly what 4 yew trees cost! So, I had a solution to the easier problem:
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My Answer
To get my solution I just needed to multiply all the numbers in the easy version of the problem by 10. This is my solution:
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3. Evaluation
I felt this problem was easy. I liked working on it because it involved money. The hardest part was finding the number of yew trees. I didn't learn anything. I'm proud I found an answer just thinking out loud.
P.S. My Dad showed me that there are ONLY 3 ways to solve this problem. It takes a long time to explain so I'll just show all the answers:
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The most important part of figuring this out is the fact that the number of oaks has to be a multiple of 5!