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# 2017 NS 29

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15 Can anyone solve this? Answer: 90.8

Mar 14, 2019
edited by dgfgrafgdfge111  Mar 15, 2019

#1
+1

L + L + 5 + 2L =36...........................(1)
L + L + 5 + 2[L + 5]=36....................(2)

From (1) above:
L =31/4 =7.75 - inches - the shortest piece
7.75 + 5 =12.75 - inches-the 2nd longest piece.
7.75 x 2 =15.5 - inches -the longest piece.
From (2) above:
L =21/4 =5.25 - inches - the shortest piece
5.25 + 5=10.25 - inches - the 2nd longest piece
10.25 x 2=20.50 - inches- the longest piece
15.50 + 20.50 =36 - inches - the sum of the longest pieces.

Mar 14, 2019
#2
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Actually, the answer was 90.8. Do you know how?

dgfgrafgdfge111  Mar 14, 2019
#3
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what is your reason for farming all the methods to solving these questions?

Rom  Mar 15, 2019
#4
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What do you mean by "farming"?

dgfgrafgdfge111  Mar 15, 2019
#5
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actively collecting, as if you intend on publishing some sort of study guide to these problems.

Rom  Mar 15, 2019
#6
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Oh, no. These are just questions that I don't have the solutions to and I can't figure out how to do them. I have attempted them already, but I keep getting the wrong answer. It's not like I'm cheating or something. I just need some help.

dgfgrafgdfge111  Mar 15, 2019
#7
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Hi Rom,

He told me that these are questions from old mathematics competitions and he is using them to 'study' from because he is going to do this type of test himself.

Melody  Mar 15, 2019
#8
+2

Case 1: 1st rope: x, 2nd rope: x+5, and the third rope 2x.

So, 4x+5=36, 4x=31, x=7.75 and 7.75*2=15.5 inches

Case 2:  1st rope: x, 2nd rope: x+5, and the third rope 2x+10.

So, 4x+15=36, 4x=21, x=21/4=5.35, and 2(10.25)=20.5 inches.

Case 3: x, 2x, 2x+5, and we have 5x+5=36, 5x=41, x=8.2 and 2(8.2)=16.4+5=21.4.

Case 4 There are other cases, maybe 2x, 4x, 4x+5 gives 10x+5=36, x=3.1 and 4(3.1)+5=17.4

This is 74.8 and there is another 16?

How about 2x, 2x+5, and 4x. 15.5?

Mar 15, 2019
#12
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You made lots of mistakes in case 3, 4, 5. They simply don't add up.

Guest Mar 15, 2019
#9
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Got it The longest peice could be     15.5,  20.5,  17.4,  16.4,   or   21          added together this is exactly  90.8 inches

So there are 5 different possibilies on how the rope is cut.   (only lenghths are important, not the order thay are cut in)

Rather than spoil everyone's fun I will let you individually work out what these 5 double cuts  are.

Hint:   Let one peice be   a   and another   a+5.      You have to work out the other one.   (5 possibilities.)

Mar 15, 2019
edited by Melody  Mar 15, 2019
#10
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Good job, Melody!

tertre  Mar 15, 2019
#11
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Thanks Tertre

You got most of it too Melody  Mar 15, 2019
edited by Melody  Mar 15, 2019
#13
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Let me see if I can figure out the possibilities:

1. a, a+5, and 2a
2. a, a+5, 2a+10
3. a, 2a, 2a+5
4. 2a,4a,4a+5
5. 2a,2a+5,4a+10
6. a+5,2a+10, 2a+15
7. a+5, a+10, 2a+20

I tried 4-7, but the results come out to be the same as 1-3. What are the other cases?

dgfgrafgdfge111  Mar 16, 2019
#14
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there are only 5 cases, of course they all total to 36

1)    a, a+5,  twice as big as the first one

2)    a, a+5,  half as big as the first one

3)    a, a+5,  twice as big as the second one

4)    a, a+5,  half as big as the second one one

5)    a, a+5 =2a,  36-3a

Mar 16, 2019
#15
+1

Oh, I see. Thank you!!!!

dgfgrafgdfge111  Mar 16, 2019