The teacher is the one who's confused here. The kid is entirely correct.
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Given 4/6 x > 5/6 y therefore x > 5/4 y
Marty's Pizza must have been more than a quarter larger than Luis'. The kid is exactly right.
And the teacher is not flexible enough to engage outside their expectations for how the question was supposed to be answered.
Clearly the expectation was for the kids to take the unstated assumption that the two pizzas were of the same size, and reject the premise as unreasonable (note the heading "Reasonableness").
This brings back memories of when I realized that I was smarter than most of my teachers.
So...
(4/6)m > (5/6)l
m > (5/4)l
Which means Marty's pizza is more than one and a quarter the size of Luis' pizza. We can comfortably just compare the area, since we can assume a flat disk with equal height for a pizza.
Assuming Luis' pizza is a Domino's Classic size of 25cm that's an area of:
(25cm / 2)² * π = (625cm² / 4) * π = 490.874cm²
So Marty's pizza should be more than 490.874cm² * 1.25 = 613.5925cm² for 4/6 of his to be greater than of 5/6 of Luis', so:
sqrt(613.5925cm² / π) * 2 = 13.975426964cm * 2 = 27.950853929cm
Since Marty's pizza is greater, let's go with 28cm diameter... which happens to match exactly a Domino's Medium size.
That's a very realistic scenario and the teacher is an absolute idiot for not understanding.
Math education in the empire is TERRIBLE. There is no actual math taught. At best it's applied analogies like this pizza BS. The teachers have never taken any advanced math so they don't even know what they're not teaching. The goals (eg. calculus) are completely worthless. The entire system is stuck in the 1700s. It's a complete failure. It's intentional too. The goal is creating obedient, little computers not critical thinkers. That would be a threat to the system. This image is just the tiniest tip of the iceberg.
There's nothing wrong with the answer.
Your fault for not listing the size and list of toppings for both pizzas, one could be a small personal pizza size with just cheese and pepperoni and the other a full huge New Yorker sized one with double of everything.
it's fairly clear there are two pizzas, but as to 'how' someone eats more than someone else... this is not really a simple math question, there are too many unknown variables. Maybe one has Bulemia, maybe one of them is 6'9" and has a much bigger appetite. Maybe one of the people has a congenital deformity resulting in two mouths... This question is not a math question, it's an exercise in creativity.
Even if it is purely a math question though, it never specifies "Their pizzas are the same size." The student literally answered how this is possible in a reasonable way that satisfies the mathematical requirements, when the teacher is expecting an impossible answer of "it's not" after saying in this scenario that Marty did in fact eat more.
Yeah, if the question was "Is this possible?" then the teacher's answer would be reasonable.
But the "how" in the question implicates that it's actually factual and the student should come of with an explanation how. Which they did perfectly.
Both of your questions would be satisfied by the student's answer though
True, even with the "Is this possible?" the student's answer should have been ok. But with the "how" the teacher's answer is plainly wrong.
How did they eat it?
They put it in their mouth, probably chewed a few times, swallowed, and then repeated the process as needed.
Q.E.D.
I know this is bait but who said they had the same-sized pizzas?
One could be XL the other one a personal pizza.