What was the person that wrote this problem thinking?

[Minoosh]

I'm a math tutor now working at a middle school. My students have a regular math class; I'm paid to help them fill in gaps in learning. This is under a COVID-related grant.

They're reviewing for a final and here is one of the practice problems:

"Mr. Jeans raises cows (x) and chickens on his farm. Altogether, his cows (x) and chickens have 140 legs. This can be represented by the function 4x + 2y = 12."

WTF? How is it not 4x + 2y = 140?

Students are told to "solve for and interpret the x and y intercepts in context," whatever that means.

But more mysteriously, why does the teacher (or whoever wrote the problem) have their students graphing the wrong freakin' line? The proper line has a y intercept of 70, not 6.

The lines are parallel, so the slope is the same.

One thing my students are almost universally bad at is turning word problems into equations. My students didn't understand why it's 4x and 2y, until I pointed out cows have 4 legs and chickens have 2. I could not convince a girl yesterday that a negative number subtracted from a negative number will be negative. "Uh-uh!" say the little miscreants. "My teacher said 2 negatives make a positive." I explained that only works for multiplication and division.

Arghh.

 

[theprestige]

Looks like someone asked ChatGPT to write a math problem, and got a mathy hallucination without realizing it.

 

[sphenisc]

I'm a math tutor now working at a middle school. My students have a regular math class; I'm paid to help them fill in gaps in learning. This is under a COVID-related grant.

They're reviewing for a final and here is one of the practice problems:

"Mr. Jeans raises cows (x) and chickens on his farm. Altogether, his cows (x) and chickens have 140 legs. This can be represented by the function 4x + 2y = 12."

WTF? How is it not 4x + 2y = 140?

Students are told to "solve for and interpret the x and y intercepts in context," whatever that means.

But more mysteriously, why does the teacher (or whoever wrote the problem) have their students graphing the wrong freakin' line? The proper line has a y intercept of 70, not 6.

The lines are parallel, so the slope is the same.

One thing my students are almost universally bad at is turning word problems into equations. My students didn't understand why it's 4x and 2y, until I pointed out cows have 4 legs and chickens have 2. I could not convince a girl yesterday that a negative number subtracted from a negative number will be negative. "Uh-uh!" say the little miscreants. "My teacher said 2 negatives make a positive." I explained that only works for multiplication and division.

Arghh.

You're going to have to convince me as well. I make -4-(-6)=2 .

 

[Thermal]

Prob just a typo, honestly.

 

[The Great Zaganza]

I'm a math tutor now working at a middle school. My students have a regular math class; I'm paid to help them fill in gaps in learning. This is under a COVID-related grant.

They're reviewing for a final and here is one of the practice problems:

"Mr. Jeans raises cows (x) and chickens on his farm. Altogether, his cows (x) and chickens have 140 legs. This can be represented by the function 4x + 2y = 12."

WTF? How is it not 4x + 2y = 140?

Students are told to "solve for and interpret the x and y intercepts in context," whatever that means.

But more mysteriously, why does the teacher (or whoever wrote the problem) have their students graphing the wrong freakin' line? The proper line has a y intercept of 70, not 6.

The lines are parallel, so the slope is the same.

One thing my students are almost universally bad at is turning word problems into equations. My students didn't understand why it's 4x and 2y, until I pointed out cows have 4 legs and chickens have 2. I could not convince a girl yesterday that a negative number subtracted from a negative number will be negative. "Uh-uh!" say the little miscreants. "My teacher said 2 negatives make a positive." I explained that only works for multiplication and division. Arghh.

I explained it with the Number Line, you probably did, too.

about the legs ... yeah, typo.

 

[Ziggurat]

"Mr. Jeans raises cows (x) and chickens on his farm. Altogether, his cows (x) and chickens have 140 legs. This can be represented by the function 4x + 2y = 12."

WTF? How is it not 4x + 2y = 140?

It absolutely should be.

I could not convince a girl yesterday that a negative number subtracted from a negative number will be negative.

Only about half the time. If the first negative number is bigger (magnitude), then it will still be negative. For example, (-8) - (-5) = (-3). But if the first number is smaller (magnitude), then the answer is positive. For example, (-4) - (-6) = +2

 

[Ziggurat]

Looks like someone asked ChatGPT to write a math problem

That is very plausible.

 

[Minoosh]

You'rH going to have to convince me as well. I make -4-(-6)=2 .

I would love to come back with a mathy retort but I can't. However, the particular problem was something like -8 - 7.

I tell them, the more you understand, the less you need to memorize. So on adding and subtracting integers, I often go back to the number line.

I should have said, "If you start with a negative number and subtract a positive number, the result will be negative," and refer them back to the number line.

 

[Minoosh]

It absolutely should be.



Only about half the time. If the first negative number is bigger (magnitude), then it will still be negative. For example, (-8) - (-5) = (-3). But if the first number is smaller (magnitude), then the answer is positive. For example, (-4) - (-6) = +2

Yes, I misspoke.

 

[sir drinks-a-lot]

Yes, back in my math days I was surprised at how many students could solve a certain difficulty of math equation, yet could not solve a word problem based upon the same equation.

I agree that it should say "4x + 2y = 140" and also agree that it was probably a typo, although a very critical one. I also just don't like the wording of the question with the X and Y in parenthesis, but that's probably just me being nitpicky.

As far as the "two negatives make a positive" canard, I think that's best understood and explained as referring to logical operators.

 

[Skeptical Greg]

Where would the typo be?

Hard to go from 140 to 12 with a typo..

I like the ChatGPT eplanation.

 

[Skeptical Greg]

Double post..

 

[Delvo]

If we could be sure that a human wrote it, I'd guess that the 12 was accidentally brought in from part of the intended answer of an intended (or formerly intended) follow-up in which they give the number of one kind of animal and ask how many there are of the other kind.

 

[Puppycow]

"Mr. Jeans raises cows (x) and chickens on his farm. Altogether, his cows (x) and chickens have 140 legs. This can be represented by the function 4x + 2y = 12."

WTF? How is it not 4x + 2y = 140?

Students are told to "solve for and interpret the x and y intercepts in context," whatever that means.

I was pretty good at math when I was a student, but it's been a long time.

If we assume that "12" is merely a typo, and should be 140, I'm not sure what it means to "solve for x and y intercepts", but there are many different combinations of chickens and cows that add up to 140 legs. If all chickens have 2 legs and all cows have 4 legs, then you could have:

1) 70 chickens and 0 cows
2) 35 cows and 0 chickens
3) 68 chickens and 1 cow
4) 34 cows and 2 chickens
and so on ...

You can replace 1 cow with 2 chickens or 2 chickens with 1 cow.
In total, there should be 35 possible solutions, which is 140/4, since 35 is the maximum number of cows, and I'm assuming only integer numbers for each animal. The number of chickens will always be either an even number or 0.

 

[Delvo]

"Solve for" is math schoolbook language for "find" or "determine" or "calculate". Solving for intercepts is finding intercepts. You did it yourself in the first post when you said one of the intercepts is 70. That was the solution you solved for. (The U and V are actually equivalent.) I shall now boldly solve for the other intercept: 35.

 

[sir drinks-a-lot]

"Solve for" is math schoolbook language for "find" or "determine" or "calculate". Solving for intercepts is finding intercepts. You did it yourself in the first post when you said one of the intercepts is 70. That was the solution you solved for. (The U and V are actually equivalent.) I shall now boldly solve for the other intercept: 35.

I think what puppycow (4 legs, I assume) was saying is that he does not know for sure what is meant by the word "intercept" in this context. I also don't quite understand what is meant. You seem to suggest it is a synonym for "solution", but I can recall having seen it used this way before.

 

[Ryan O'Dine]

The equation is even wronger than that, unless there are literally no chickens or cows that are pregnant.

 

[Delvo]

I think what puppycow (4 legs, I assume) was saying is that he does not know for sure what is meant by the word "intercept" in this context. I also don't quite understand what is meant. You seem to suggest it is a synonym for "solution", but I can recall having seen it used this way before.

I was about to say that the posts I was responding to had already shown an understanding of the word "intercept(s)", but now I see that, although they both said they didn't know what "solve for intercepts" meant, they were by two different people, which means they could have two different sources of confusion/uncertainty.

In the first post, Minoosh solved for an intercept and said it's 70, so (s)he knows what intercepts are and must have been thrown by the "solve for" expression.

In the more recent post, Puppycow does some math which doesn't involve intercepts, so it's possible that Puppycow was thrown not by the "solve for" part, but by the "intercept" part.

An intercept is a point at which an equation's graph crosses (intersects/intercepts) one of the two axes: the x-axis or the y-axis. Every sloped straight line has exactly two, one on each axis, unless it goes through the single point where both are zero. A parabola can have one, two, or three of them depending on its location & orientation. A hyperbola has none. A sine or cosine wave always has one intercept on one axis and zero or infinity intercepts on the other axis (because if it crosses, for example, the y-axis once, then it crosses the x-axis either never at all or over & over again on every cycle). But in all cases, they're one of the first & easiest things you can do with a complicated graph, because one of the variables (x or y) is zero.

So, with "solve for" meaning "find", you solve for intercepts by putting in zero for one of the variables and finding what they other one must be from the equation. In the story problem with cows & chickens, they are the solutions that consist of all one type of animal and none of the other.

 

[Ziggurat]

I think what puppycow (4 legs, I assume) was saying is that he does not know for sure what is meant by the word "intercept" in this context.

It's the point where the line given by the equation crosses (intercepts) the x or y axis. So the equation 4x + 2y = 12 intercepts the x axis at (x=3,y=0), and it intercepts the y axis at (x=0,y=6).

 

[Puppycow]

Thanks. It was the word "intercept" that confused me, but I understand now what it means. The number 12 is clearly erroneous. Doesn't agree with the number given in the word problem.