Math question | important

[serene swift]

Rodrigo plays with a two-meter tape, with centimeter-by-centimeter marks. Starting at the end marked 0 cm, he folds the tape several times in a zigzag pattern, as shown in the figure, overlapping pieces of tape of the same size until he folds the last piece, which may be smaller than the others. He notes that the 49 cm and 71 cm marks overlapped on neighboring pieces. He also notes that the 139 cm mark lined up with them and the end of the tape overlapped with a mark from the penultimate piece. With that in mind, check the expression that represents this brand.

Options in the image!!

[slow summit]

what is "the expression that represents this brand"

[serene swift]

Sorry, in context it is mark/marking

[slow summit]

what am i meant to find here i have no idea

the height of the thing?

[serene swift]

I don't know

[serene swift]

To find the expression that represents the mark where the end of the tape overlapped

[slow summit]

ah ok

thanks

[slow summit]

alright so for these types of problems you want to create a variable and solve for it

what variable should be created?

what single piece of missing information would solve this problem

[serene swift]

i have no idea how to solve

[slow summit]

what about how long one of the segments is

[serene swift]

Sorry, I don't know

[slow summit]

ok so I’ll give you a hint

assume the length of this is x

try to make an equation for x with the information given

[serene swift]

Ok, thanks

[half marsh]

@serene swift has given 1 rep to @slow summit

[serene swift]

I couldn't solve it at all

[slow summit]

green is 49 red is 71
note that there will be a distance of 11 to a side (can be the right one as well)

and 139 is above them

so 139 is also 11 away from a side (the same side)

@serene swift another hint

[serene swift]

I think it's E or C

A) 2⁴ . √4 . 5

B) 2³ . √4 . 11

C) 2 . √25 . 19

D) 2² . √49 . 7

E) 2² . √4 . 23

The answer is E) 2² . √4 . 23.

Let's analyze the problem step-by-step.

The tape is 2 meters long, so it has 200 centimeters.
The 49 cm and 71 cm marks overlap, so the first fold is at 22 cm.
The 139 cm mark aligns with the 49 cm and 71 cm marks, so the second fold is at 98 cm.
The final end of the tape overlapped with a mark from the second to last piece, so the last fold is at 116 cm.
The expression that represents this mark is 2² . √4 . 23, or 219.
Here is the explanation:

The first fold is at 22 cm, which is 2² . √4.
The second fold is at 98 cm, which is 2³ . √4.
The last fold is at 116 cm, which is 2² . √4 . 23.
Therefore, the expression that represents this mark is 2² . √4 . 23.

[slow summit]

how does this make any sense >:(

the answer is also wrong as they specify the folds are the same size
22≠98-22

tf

[serene swift]

Sorry for the previous error. The correct answer is the letter C.

Here is the solution:

1. The ribbon length is 2 meters, or 200 centimeters.
2. The 49cm and 71cm marks overlap, so the first fold point is at 22cm.
3. The 139 cm mark lines up with the 49 cm and 71 cm marks, so the second fold point is at 98 cm.
4. The last fold point is half the length of the tape between the second fold point and the 139 cm mark, or 190 cm.

Here is the explanation of the expressions:

• E: 2² * √4 * 23 = 4 * 2 * √4 * 23 = 16 * 2 * 5.83 = 184
• C: 2 * √25 * 19 = 2 * 5 * 19 = 10 * 19 = 190

Therefore, the correct answer is the letter C.

[slow summit]

is that chat got

gpt

[serene swift]

Yess

[slow summit]

chatGPT is horrible at math

lm explain I have the basic solution done

[serene swift]

Google bard

[serene swift]

Okk

[slow summit]

don’t use AI for math

or like

problem solving

simple arithmetic yes

[serene swift]

Ok

[slow summit]

so each of these points is a multiple of x

[slow summit]

and since 49 and 71 are neighbours, they touch like this

with a distance of 11 to one multiple of x

49+11=60

so x is a factor of 60

note that x must be greater than 11 or else 49 and 71 would not be neighbours

so the factors of 60 left are 15 20 30 60

now let’s consider 139

139 is also 11 away from a multiple of x

it can’t be 11 after or else there wouldn’t be any common factors

so it’s 11 before a multiple of x

139+11=150

so we get
15 30 left

uhh there’s probably a way to tell which one it is

yea it can’t be 30

so note that 2x is always on the left side

49 and 71 are closer to 60

so 139 most be 11 away from 150

150 however is on the right side

so it’s 15

x is 15

finally we find where 200 intersects

195 is the last fold

so it intersects 190

wow chat gpt actually got it
although it’s solution makes 0 sense

@serene swift do you understand

I went a bit fast

lmk if there’s any part you want me to explain further

[serene swift]

Yes, that was incredible, the correct one was the letter C, right? As you said, he gave the answer in a meaningless explanation!

[slow summit]

yea it’s C

you should try double checking tho

assume each fold has length 15 and see if the marks match up

so quick recap of the solution
I made a variable x I wanted to find
then used the information to try and find x

noting that each fold was a multiple of x

was basically the main thing you have to realize

and that 49 and 71 are equidistant from some multiple of x

hope you learned soemthing