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| To begin a problem, not only do you have to identify what it is that you are trying to find out, you must identify what you know for sure and work from there. In the example below we are told that Chuck has 3 red geraniums in his garden. Knowing this allows us to calculate how many geraniums Spike has in his. Chuck's 3 geraniums + 6 (more) = Spike's 9 geraniums. |
| Chuck and Spike enjoy growing flowers in their gardens. Unfortunatley an early frost damaged their geraniums. Spike was left with 6 more than Chuck. Chuck, after checking the damage, realized that he had only three geraniums left. How many geraniums does Spike still have? |
| Making use of a chart is often helpful in finding the solution to a problem. In the example below we are told that Chuck has 3 geraniums in his garden. All of the other characters' geranium quantities are related to each other. The following chart makes the relationships clear. Start with what you know for sure. |
| Gardener | # of Geraniums |
| Chuck | 3 (we were told this) |
| Gertrude | 2XChuck(3) = 6 |
| Samantha | Gertrude(6)-4(less)= 2 |
| Spike | Samantha(2)+6(more)= 8 |
| Chuck, Gertrude, Samantha and Spike enjoy growing flowers in their gardens. Unfortunatley an early frost damaged their geraniums. Spike was left with 6 more than Samantha. Samantha had 4 less geraniums survive than Gertrude. Gertrude had twice as many left as Chuck. Chuck, after checking the damage, realized that he had only three geraniums left. How many geraniums does Spike still have? |
| Drawing pictures can be very helpful. Looking at the Geranium 2 problem below we see that we should again start with what we know for sure, that is, Chuck has three geraniums. The illustrations below the problem help show the problem's solution. |
| Chuck, Gertrude, Samantha and Spike enjoy growing flowers in their gardens. Unfortunatley an early frost damaged their geraniums. Spike was left with 6 more than Samantha. Samantha had 4 less geraniums survive than Gertrude. Gertrude had twice as many left as Chuck. Chuck, after checking the damage, realized that he had only three geraniums left. How many geraniums does Spike still have? |
 |
| Chuck |
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| Gertrude= 2 times Chuck = 6 |
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| Samantha = 4 less than Gertrude = 2 |
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| Spike = 6 more than Samantha = 8 |
| Sometimes a problem will not give you an obvious starting point. It will not tell you anything for sure about the characters. In these cases you may guess and then check you answer. In the problem below we know the total, but this is not enough information. If we guess that Chuck has five we then work throught the relationships. (see charts) |
| Chuck has 3 more geraniums than Fred. Fred has six less than Martha. Martha had five more than Spike, but two were stolen. If the total geraniums that they have is twenty-eight, how many geraniums does Chuck have? |
| Gardener | # of Geraniums |
| Chuck | 5 (a guess) |
| Fred | 2 (3 less than Chuck) |
| Martha | 8 (6 more than Fred) |
| Spike | 5 ((5-2)=3 less than Martha) |
| Total | 20 (not 28) try again |
| Gardener | # of Geraniums |
| Chuck | 6(a guess) |
| Fred | 3(3 less than Chuck) |
| Martha | 9(6 more than Fred) |
| Spike | 6 ((5-2)=3 less than Martha) |
| Total | 24 (not 28) try again |
| Gardener | # of Geraniums |
| Chuck | 7 (a guess) |
| Fred | 4 (3 less than Chuck) |
| Martha | 10(6 more than Fred) |
| Spike | 7 ((5-2)=3 less than Martha) |
| Total | 28 we're right |
| Some problems do not deal with numbers, but only with relationships. To answer these the use of a logic array (chart) can be helpful. Check off the matches. If there are no conflicts then you are correct. |
| Fred likes the colour of flowers that is in his name. Martha likes the colour that no of the other girls like. Samantha likes the colour that Spike doesn't. Spike won't have anything in his garden that is orange. Ruggles likes her garden to match the sky. If no character has the same colour as another and the colours are Blue, Red, Orange and Yellow, match the colours with the characters. |
| Blue | Red | Orange | Yellow | |
| Fred | no | yes | no | no |
| Martha | no | no | no | yes |
| Samantha | no | no | yes | no |
| Ruggles | yes | no | no | no |
| Since Fred likes the colour in his name , he must like Red. Therefore a no is placed beside Fred and under Blue, Orange and Yellow. Since Spike won't have anything in his garden that is orange, then he gets a no under orange and Samantha gets a yes under orange. Blue matches the sky better than yellow, so Ruggles gets blue. That leaves yellow for Martha. |
Algebra
involves representing a number with a letter or
word. Making use of algebra may help you
solve problems. In the following problem
Ruggles' geraniums can be represented in the
following algebraic statement:
|
| Ruggles has 40 more than twice as many geraniums as Martha. If Martha has 50 Geraniums, how many does Ruggles have? |
