Wednesday, January 27, 2010

Question #2: The carpenter and the missing stairs

A carpenter is replacing some missing steps at the front of Dena’s house. The bottom three steps are missing. He wants to use the same heights for the new steps as the old steps. The carpenter measures the height from the ground to the top of each remaining step.


• The fourth step is 66 cm from the ground.
• The fifth step is 82.5 cm from the ground.
• The sixth step is 99 cm from the ground.





The carpenter plans to make each step increase by the same amount. What are the heights of the first, second and third steps? Show your work and explain.

15 comments:

  1. Each step increases by 16.5cm. Therefore the third step is 49.5cm high,( 66cm - 16.5cm = 49.5 cm.) The second step is 16.5cm lower or 33cm high, (49.5cm - 16.5cm = 33cm.) The first step from the ground is 16.5cm high,(33cm - 16.5cm = 16.5cm.)

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  2. the number that it increases by is 16.5 66+16.5=82.5 and 82.5+16.5=99
    the first stair is 16.5 and 16.5+16.5=33 and 33+16.5=49.5 and 49.5+16.5=66 so my method is correct.

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  3. I noticed that in each stair height there was a pattern. If you minus the first stair by thesecond stair, you get 17.5 If you minus the second stair by the third stair you get 16.5 So if you were to minus 66 (the third stair) by 15.5 you would get6 your answer. The pattern i found, was when you minus the first number the second, and keep going down the list the number goes down by one each time. So the forth stair down would be 51.5 cm, the fifth step would be 37 cm, and the sixth step would be 24.5 cm (i counted the steps from right to left, not left to right!)
    ~Iris

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  4. what i did was first i subtract 99cm by 82.5cm= 16.5cm, then i did 82.5cm-66cm=16.5cm, which means i know each time it goes up by 16.5cm. so then i took 66cm-16.5cm=49.5cm, the 49.5-16.5cm=33cm, then 55cm-16.5cm=16.5cm
    so the last tree stps are 49.5cm, 33cm, and 16.5cm.

    Adele

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  5. Each step increases by 16.5cm each time. I found this by subtracting the 5th step from the 6th step. The third step is 49.5cm. The 2nd step is 33 cm. The 1st step is 16.5cm.

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  6. Hey everyone,
    So first I looked at the difference between the steps still standing (top 3). The difference between 66 and 82.5 is 16.5 and the difference between 82.5 and 99 is 16.5. The number that the steps increase by is 16.5.

    Next, I subtracted 16.5 from 66 to get 49.5. Then I subtracted 16.5 from 49.5 to get 33. Then when I subtracted 16.5 from 33, I got 16.5.
    So the first step in 16.5 cm. The second is 33 cm. The third is 49.5 cm.
    Katty

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  7. the pattern is -16.5cm each time. i know this because 99cm - 82.5cm = 16.5cm, and 82.5cm - 66cm = 16.5cm.

    therefore,
    66cm - 16.5cm = 49.5cm (step #3)
    and 49.5cm - 16.5cm = 33cm (step #2)
    and 33cm - 16.5cm = 16.5cm (step #1)

    -jeff

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  8. The height increases by 16.5cm each time. But because the top 3 are given to you, you have to work backwards, which is what i did. first, i subtracted 99-82.5. I got 16.5. so then i subtracted 82.5-16.5=66. So i found out that i had the right number. The i kept on subtracting and came to this conclusion.
    6th step is 99cm
    5th step is 82.5cm
    4th step is 66cm
    3rd step is 49.5cm
    2nd step is 33cm
    1st step is 16.5cm
    Then, i checked over my answer by starting at the first step and adding

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  9. I started by finding the difference between the steps. 99cm-82.5cm=16.5cm
    82.5cm-66cm=16.5cm. So I decided to do 66cm-16.5cm= 49.5cm
    49.5cm-16.5=33cm
    33cm-16.5cm=16.5cm

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  10. The first step is 16.5cm. The second step is 33cm. The Third step is 49.5cm. I found this by looking for the difference between the steps. The difference is 16.5cm. If you keep adding on the 16.5s from the zero you will get the fourth, fifth and sixth steps heights. This is how I got the answer.

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  11. First I subtracted the height of step 5 from step 6. (99cm-82.5cm) Which equals 16.5 cm. Then I double checked with the fourth step. So the height of the third step = 66cm -16.5cm =49.5cm. Then the height of the second step is 49.5 - 16.5 =33cm. The height of the first step is equaled to 33cm - 16.5cm = 16.5. Therefore all the steps increase by 16.5 cm.

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  12. heyyyy sup ma bois anywayz i dunno how thiz is possible so easy so ima say that each tile 10cm2x10cm2 is 100cm2 and 100cm is a metre so then 5m2x10m2 is 50m2 and so i guess 50 tiles is 50 metres so 50 beowulf tiles. from the mught gonthorian and his sidekick wonder woman.

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  13. omg lolz they both seem to be ez so i guess each time it increases by16.5 so i gues the 3rd is 49.5 and then 33 b4 that and the first is 16.5 yay cya later pplz from might mg

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  14. 99cm-82.5cm=16.5cm
    step 3=49.5cm
    82.5cm-66cm=16.5cm
    step 2=33cm
    66cm-16.5cm=49.5cm
    step 1=16.5cm
    49.5cm-16.5cm=33cm

    33cm-16.5cm=16.5cm

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  15. well i did 99-82.5 to see the diffrence its 16.5
    then 82.5-66= 16.5 so the diff is 16.5
    to see the missing steps i would subtract the diff from the number
    66-16.5=49.5 the third step is 49.5 cm high
    49.5-16.5=33 the second step is 33 cm high
    33-16.5=16.5 the last step is 16.5 cm high

    p.s the raps are down in indy 106 to 87 10:00 remaining in the 4th

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