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Problem
Solving Strategy |
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Solution |  |
1. Mary has 6 coins, which have a total value of 67 cents. What combinations of coins could she have? Use denominations of 1�, 5�, 10� and 25�.
| Penny 1� | Nickel 5� | Dime 10� | Quarter 25� | Total |
| 2 | 1 | 1 | 2 | 6 |
2. Navigate your spaceship to the "Black Hole". The product of the numbers along your path must be 2592.
| Start | ||||||||
| 6 | ||||||||
| 2 | 10 | |||||||
| 3 | 4 | |||||||
| 9 | 2 | |||||||
| 7 | 1 | |||||||
| 8 | 2 | |||||||
| 4 | 5 | Black Hole |
2 x 3 x 6 x 4 x 9 x 2 = 2592
3. The sums of numbers on each side of the magic triangle are all the same. Find two solutions for the magic triangle using a different number in each box.
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Sum = 10 + 24 + 16 = 50 | ||||||||
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A + B = 40 & B + C = 32 | |||||||
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Fix a number for B and the will | |||||||
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difference from the above sums | |||||||
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yield A and C |
4. a) How many shots at this target are needed to make a score of 300?
b) Find four different combinations where the value of the shots on the target totals 300.
| Numbers | 45 | 48 | 51 | 54 | 57 | Total |
| No. of shots | 0 | 3 | 2 | 1 | 0 | 300 |
| No. of shots | 2 | 1 | 1 | 1 | 1 | 300 |
| No. of shots | 2 | 2 | 0 | 0 | 2 | 300 |
| No. of shots | 2 | 1 | 0 | 3 | 0 | 300 |
5. If r is less than 10, what value of r makes r3749r0 divisible by 60? (there are two possibilities.)
r3749r0 � 60 ====> r3749r � 6
A number divisible by 6 is even and divisible by 3.
So r must be even and r3749r is its divisibility by 3.
3 + 7 + 4 + 9 = 23
23 + r + r is divisible by 3 and r < 10 and even
===> r = 2 and 8
6. Find a set of 3 consecutive even numbers whose sum is 294.
294 � 3 = 98
| 98 - 2 | 98 | 98 + 2 |
| 96 | 98 | 100 |
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