Multiple Variables Question

N

Necco

New member
Joined
Aug 19, 2021
Messages
3
Hello,

During math class, we had a practice question that no one (including our math teacher) knew the answer too. I have provided a screenshot of the question along with the answer choices below (The purple thing below is the timer). The correct answer to the question is 64, but none of us know why it's 64. I was wondering if there was anyone who could explain why 64 is the correct answer as well as a math formula that can help me and others with this problem? If there happens to be an error with the question, let me know!

Thank you!
IMG_0810.jpg
 

Attachments

  • image1.jpeg
    image1.jpeg
    31.7 KB · Views: 1
Necco said:
Hello,

During math class, we had a practice question that no one (including our math teacher) knew the answer too. I have provided a screenshot of the question along with the answer choices below (The purple thing below is the timer). The correct answer to the question is 64, but none of us know why it's 64. I was wondering if there was anyone who could explain why 64 is the correct answer as well as a math formula that can help me and others with this problem? If there happens to be an error with the question, let me know!

Thank you!
View attachment 28604
Click to expand...
I am assuming that each shape represents numbers. Any other information available - like

Do the shapes represent non-negative integers?​
​
Do the shapes represent numbers in real domain?​
 
Subhotosh Khan said:
I am assuming that each shape represents numbers. Any other information available - like

Do the shapes represent non-negative integers?​
​
Do the shapes represent numbers in real domain?​
Click to expand...
I don't know, but I'm assuming they can be either one since the question didn't make that clear. The shapes are like variables (x,y,z), so certain numbers need to be plugged in order for all of the equations to be answered.
 
no the equation is not complete
if you turn the shapes to variables you get
x + y - z = 15
and
y*z = 18
but x is independent from second equation
so you can get any answers for y and z that makes second equation true
and then calculate the needed x in first equation,
so the question is missing some clarification


this is some examples of the answers
x = 8 , y = 9, z = 2
x =12, y = 6, z = 3
 
Necco said:
Hello,

During math class, we had a practice question that no one (including our math teacher) knew the answer too. I have provided a screenshot of the question along with the answer choices below (The purple thing below is the timer). The correct answer to the question is 64, but none of us know why it's 64. I was wondering if there was anyone who could explain why 64 is the correct answer as well as a math formula that can help me and others with this problem? If there happens to be an error with the question, let me know!

Thank you!
View attachment 28604
Click to expand...
Note, that the question is which choice can't be the question mark.
If it's 64, then what about 32, 1, 18 as the values of shapes in the first equation? They work for the first 2 equations and make the question mark 64.
 
yes any solution to third equation = h
will turn to be a root for this equation
y3 - 14y^2 + (h - 33)y -18 = 0
where y is the second shape
 
Necco said:
Hello,

During math class, we had a practice question that no one (including our math teacher) knew the answer too. I have provided a screenshot of the question along with the answer choices below (The purple thing below is the timer). The correct answer to the question is 64, but none of us know why it's 64. I was wondering if there was anyone who could explain why 64 is the correct answer as well as a math formula that can help me and others with this problem? If there happens to be an error with the question, let me know!

Thank you!
View attachment 28604
Click to expand...
Lev888 has shown (#7) that 64 is NOT the correct answer, because it IS possible to get ? = 64:
  • 32+1-18 = 15
  • 18*1 = 18
  • 1*32+32 = 64
So your information is wrong.

My guess has been that the symbols all represent integers, and you are supposed to use some sort of number theory (e.g. if the answer had to be a multiple of 3, 64 wouldn't work). I can show that "?" has to be even, but that doesn't help.

What course are you taking, and where did the problem come from? (Is it related to the course, or just a random problem from some website?)

EDIT: No, it's simpler than I thought. List all possibilities for square and circle (factors of 18), and for each determine from the first equation what heart is. For each, determine "?", and one will be not in the list. (It is not 64.)
 
Last edited:
Necco said:
The correct answer to the question is 64 ... If there happens to be an error with the question, let me know!
Click to expand...
Hi Necco. The error is with the given answer (64). The correct answer is one of the other numbers. We could start with factors of 18 for Square and Circle and then determine Heart for each case. Using those results, we could then check each of the given choices, using the third equation. One of them doesn't work.

?
 
AbdelRahmanShady said:
... you can get any answers for y and z that makes second equation ... so the question is missing some clarification
Click to expand...
I think you've misread the exercise, Abdel. We're not asked to solve the system. We're asked to eliminate one of the given choices.

?
 
Oh wow. There were only six posts, when I started my reply. I didn't get the usual heads-up from the system (or they disappeared while I was outside for a smoke).

:rolleyes:
 
If we want to eliminate results the question must specify that x and y are integer factors of 18 or something
 
We're always free to experiment! If we were to try something that yielded all of the choices except one of them, then it would be natural to think that we were on to something.

Besides, did you attempt to solve your cubic equation? It gets really messy. That would make me think that I was missing something.

;)
 
AbdelRahmanShady said:
If we want to eliminate results the question must specify that x and y are integer factors of 18 or something
Click to expand...
If you're saying that the problem was not clearly stated, I fully agree that it fails to mention integers. But it does explicitly mention elimination.

It appears to be more of a puzzle than a proper math problem, in the sense that you have to figure out what is meant. (Real life is full of puzzles, so they can be good learning opportunities.)

In addition, I asked the OP about context, because that often helps in interpreting puzzles. I doubt it would really help here, since the student appears to be thinking in terms of systems of equations in several variables, so the context is an algebra class, though the puzzle is more about factoring.
 
AbdelRahmanShady said:
the question must specify that x and y are integer factors of 18
Click to expand...
I was able to answer the question without having that specification.

In order to avoid pages of messy algebra, I had tried at first various substitutions, trying to find a useful simplification (i.e., I did experimentation). It wasn't happening, so I started considering cases, and the first one worked.

Sometimes, we have to make assumptions because that's the only way to reasonably solve the exercise.

?

PS: I'm curious to know why the instructor got stuck. I'm also curious to know whether that school provides all students with smartphones, so that everyone is able to participate in class discussions that use an app with a timer. (Something seems off.)

[imath]\;[/imath]
 
You must log in or register to reply here.
Top