| Original Problem: | Fill in the blanks using the numbers: $3.20, 12, 3, 40 cents, $1.80, 1, $1.20, 6 Donuts cost _______ each. If you buy ___ you will pay _____. However, a special rate of _____ is given for ___ donuts and _____ is the special price for ___ (called ___ dozen). |
1. Problem Statement
This problem is called The Donut Shop. The problem starts with a bubble with some numbers listed in it. Then there is a paragraph with some blanks in it. The paragraph is about how much donuts cost. You are supposed to put the numbers in the blanks to make the paragraph make sense.
2. Process
To prepare to solve the problem I studied and read it all carefully. The information I used was the list of numbers and the meanings of the sentences. The strategy I tried was to make organized lists of possible numbers for each blank and to think about which ones made sense.
The first thing I did was to make a list of all the possibilities.
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| Donuts cost _____cents each |
1, 3, 6, 12, 40 |
You can't have a decimal point in cents. |
| If you buy _____ |
1, 3, 6, 12, 40 |
You can't have decimal point in number of donuts. |
| you will pay $_____. |
1.20, 1.80, 3.20 |
You must have a decimal point in dollars. |
| a special rate of $_____ |
1.20, 1.80, 3.20 |
You must have a decimal point in dollars. |
| for _____ donuts |
1, 3, 6, 12, 40 |
You can't have decimal point in number of donuts. |
| and $_____ is the |
1.20, 1.80, 3.20 |
You must have a decimal point in dollars. |
| price for _____ |
1, 3, 6, 12, 40 |
You can't have decimal point in number of donuts. |
| (called _____ dozen.) |
1, 3, 6, 12, 40 |
You can't have decimal point in number of dozen. |
The number of donuts you buy times the price of each donut is how much you have to pay. So the first number times the second number had to be equal to the third number. So I multiplied all the possible combinations together.
The only ones that worked are 40cents x 3 = $1.20 and 3cents x 40 = $1.20. It didn't make sense to get a donut for 3cents. So the first number had to be 40cents. The second number had to be 3 and the third number had to be $1.20. This used up the numbers 3, 40 and 1.20 so they couldn't be used any more. I crossed them off the list everywhere.
There are 12 donuts in a dozen and the biggest number left was 12. So the last number had to be 1 dozen. That meant that the number before that had to be 12. Since 1, 3, 12 and 40 were all used up, the only whole number left for the fifth number was 6. Now my list looked like this
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Numbers |
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| Donuts cost _40_cents each |
This is the only answer that makes sense. |
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| If you buy _3_ |
This is the only answer that makes sense. |
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| you will pay $_1.20_. |
1.20, |
This is the only answer that makes sense. |
| a special rate of $_____ |
You must have a decimal point in dollars. These are the only ones left. |
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| for _6_ donuts |
This is the only answer that makes sense. |
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| and $_____ is the |
You must have a decimal point in dollars. These are the only ones left. |
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| price for _12_ |
This is the only answer that makes sense. |
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| (called _1_ dozen.) |
1, |
This is the only answer that makes sense. |
The last two numbers were easy. The price for 6 donuts must be less than the price for 12 donuts. So the fourth number had to be 1.80 and the sixth number had to be 3.20.
The Answer
Donuts cost 40 cents each. If you buy 3 you will pay $1.20. However, a special rate of $1.80 is given for 6 donuts and $3.20 is the special price for 12 (called 1 dozen).
3. Evaluation
I felt that this problem was simple. I liked it because I was familiar with the kind of problem. The hardest part was finding out the special rates in the middle of the paragraph. I learned how to make a list of possible answers and find the right ones. I'm proud that I solved this problem before Monday.