Internet is going wild over this problem

hey this is press tow Walker this problem took the Internet by storm in 2016 and still makes surrounds nearly every year problem number eight reasonableness Marty at 46 of his pizza and LS ate 56 of his pizza Marty ate more pizza than Lewis how is that possible the student who answered this question gave the response that Marty's Pizza is bigger than Lois's pizza so there should be no controversy this is definitely a reasonable answer but the controversy started because the teacher marked this reply as wrong the teacher even then wrote that is not possible because 5 over 6 is greater than 4 over 6 so Lois ate more I thank ranan for the suggestion now let's just try to reason what the teacher might have been thinking if the pizzas were the same size we could compare Marty's Pizza to Lois's Pizza let's divide both pizzas into six slices now four six of the pizza will be four of the slices and then five six of Lois's pizza will be five of these slices so clearly there's no way that Marty could have eaten more than Lois if the pizza pizzas were the same size but there's nothing in the question saying the pizzas have to be the same size certainly we can imagine increasing the size of Marty's Pizza and eventually at some point four slices of a very large pizza will be more than five slices of a smaller pizza so it is completely reasonable that Marty's Pizza is bigger than Lois's pizza and therefore Marty ate more pizza than Lois the students reply was completely correct and unfortunately the teacher marked it wrong the question sparked a lot of outrage online and not just from Educators and mathematicians but also from food blogs and even the larger media the question sparked its fair share of memes where people were showing how Marty's Pizza could be gigantically sized compared to Lois's Pizza in any case returning to the problem at and we have a mathematical question how much bigger does Marty's Pizza need to be so that 46 of Marty's Pizza is at least as large as 56 of Lewis's pizza so many times pizza sizes are given by the diameter of the pizza but we need to know the area of the pizza and this formula is in terms of the radius so let's let the radius be equal to half the diameter let's do these variables for both of the pizzas so the larger Pizza will have an area ofk * R 2 the radius will be equal to half the diameter and then when we Square the numerator and denominator and multiply by pi this works out to be Pi d^2 / 4 the same formula will be true for the smaller Circle we just use the corresponding variable for the smaller Circle so we go ahead and apply this formula and we end up with a very similar formula so now let's compare how much Marty ate to how much Lois ate so Marty ate 4 six of his pizza and Lois ate 56 of his pizza we need Marty to eat at least as much as Lois so we have a greater than or equal to here now let's simplify this inequality the pi terms will cancel out because pie is baked into both formulas we can now cancel out the denominators of four and the denominators of six this simplifies to be four multiplied by large d^2 is greater than or equal to 5 multili little d^2 we can divide both sides by Little D squ and by four to get the following inequality and then we just need to take the square root of both sides since all variables we're dealing with are non- negative we can safely take the square root of both sides so we have have the ratio of diameters must be greater than or equal to < TK 5 / 2 so what does that mean in Practical terms < 5 / 2 is approximately equal to 1. 18 that means Marty's Pizza must be larger by about 11. 8% so let's put that in Practical terms if Lois orders a small 10-in pizza Marty's Pizza has to be at least 11.

18 in if Lo's Pizza is a medium 12in Pizza Marty's Pizza must be at least 13. 42% than Lois's 56 share it's not that hard for Marty to order a larger pizza and eat more pizza than Lois now while we're on the topic of pizza I want to share another interesting little tidbit you can compare pizza sizes just by comparing the ratio of their diameter squared this is convenient because pizzas are often quoted in terms of their diameter size so let's see why this is true so let's compare Mar pizza's area versus Lois's Pizza area so we have Pi multili Big R 2 / Pi multili little R 2 the pi terms will cancel out so we just have the squared ratio of the radi each radius is equal to its diameter / 2 so when we Square this out we end up with d^2 / 4 divid little d^2 / 4 the fours will cancel out so we just end up with the ratio of the diameter squared so it's a very convenient way that we can compare pizza sizes you don't have to worry about multiplying by pi and you don't have to worry about converting the diameters into radi you just compare the square of the ratio of the diameters so let's apply this formula in a practical setting so let's say you have an 18-in pizza and you have two 12-in pizzas which one is larger now most people will opt for the 212 in pizzas but let's do the math let's compare an 18-in Pizza to a 12in pizza all we need to do is take the square of the ratio of the diameters so we take the square of 18 / 12 18 / 12 is equal to 1. 5 then the square of 1.

5 is equal to 2. 25 this means that 18in pizza has 2. 25 times the area of a 12 in p Pizza in other words an 18in Pizza is larger than two 12 in pizzas now you could also go through the entire calculation and see this directly but in this case you have to worry about converting the diameter into the radius and you have to multiply by pi and you end up with an approximate answer you can see that an 18-in Pizza is larger than two 12in pizzas here's a similar counterintuitive fact let's say you have a 14in pizza or two 10in pizzas many people would think the two 10in pizzas are much larger but let's do the math if we compare the square of the ratio of the diameters we get the square of 14 / 10 is equal to 1.

96 in other words the 14-in pizza has 1.