r/theydidthemath 1d ago

[Request] Which is a better deal?

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1.4k

u/Lomega18 1d ago

So, the 6 inch Pizza has an area if

62*pi=113 sq. inch * (65/360)=20.4 sq. Inch

the pizza with 7 inch has

72*pi=154 sq. Inch * (45/360)=19.2 sq. inch.

Get the 6 inch, it has abut 1.2 Square inches more pizza for 20 cent less :)

270

u/babysharkdoodood 1d ago

It's so weirdly cut though, another slice on that pizza might be huge though.

117

u/dwaynebathtub 1d ago

2/11 chance you get the 32.5-degree slice on the 6-inch pizza. Keep your eyes peeled and don't be afraid to ask for a measuring tape.

42

u/CipherWrites 1d ago

whip out your handy protractor

46

u/SmegB 1d ago

Last time I did that it lead to a protracted argument. We were divided

26

u/CipherWrites 1d ago

Might have to approach it from a different angle then

9

u/No-8008132here 1d ago

I need a pie chart

3

u/thekoreanswon 1d ago

Is that aligned with your moral compass?

2

u/Potential_Drawing_80 1d ago

It was the root of the sin, boobs.

u/MovinOnUp2TheMoon 7m ago

Did you turn the calculator upside down for that result?

2

u/Long_jawn_silver 11h ago

don’t be obtuse

2

u/TheLostTexan87 22h ago

That's not all I'm whipping out.

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u/Level9disaster 1d ago

Imagine a non Euclidean pizza on a hyperbolic surface.

15

u/simplysimonm 1d ago

I literally can't.

10

u/ghettoeuler 1d ago

Well then imagine someone who could Imagine a non Euclidean pizza on a hyperbolic surface.

7

u/MistahBoweh 1d ago

Imagine a world where a man can imagine a non-euclidean pizza on a hyperbolic surface, hurtling through time and space on a crash course with the hungry maw of entropy. This is… the twilight zone.

1

u/Derbloingles 1d ago

Prompt engineering be like

4

u/TopSecretSpy 1d ago

In other words, how it came the one time when I UberEats'd one.

Damn things looked like the driver came on horseback and put the whole box under the saddle like cowboys used to do to soften their jerky.

6

u/cpafa 1d ago

Just dip them both in water and see which displaces more. Buy the bigger wet piece. If you get lucky, they may give you both.

3

u/WolverinesSuperbia 1d ago

And 9/11 chance you don't

5

u/No-Software9734 1d ago

Yes, it would be much more logical if it was 60 degrees.

Now the first pizza is: 1.50 / ( 62 * pi * 65 / 360) = 0.0735 dollar/inch2

Otherwise the first pizza is: 1.50 / ( 62 * pi * 60 / 360) = 0.0796 dollar/inch2

And the second pizza is: 1.70 / ( 72 * pi * 45 / 360) = 0.0883 dollar/inch2

It is much closer if the first pizza would be 60 degrees (1/6)

2

u/WanderingFlumph 1d ago

45 degree angle: okay that is just 1/8th of pizza circle

65 degree angle: okay who cut a pizza into 13/72 ths? I just want to talk...

0

u/Intergalactyc 7h ago

Actually the angles listed are wrong - measuring the image, they're really 45 and 36 degrees, which sensibly divide the pizza into 8 and 10 slices respectively!!!

57

u/Business-Emu-6923 1d ago

You can just do chaotic maths and ignore the common factors:

6x6x65 =2,340

7x7x45 =2,205

43

u/NoBusiness674 1d ago

Most cursed unit: °"² (degree inch squared)

5

u/Lihiro 1d ago

I'm cringing looking at it. Take it away!

2

u/Business-Emu-6923 1d ago

Degree inch squared is the only measure of pizza you need.

1

u/meIpno 1d ago

°"° tiny face

5

u/sneakyhopskotch 1d ago

You should then divide by the prices to make sure of the answer. Love it though.

5

u/Level9disaster 1d ago

No need, as the first one is also cheaper.

5

u/sneakyhopskotch 1d ago

Ture. I should have said "to be sure of how much of a better deal it was"

2

u/Ignorhymus 1d ago

Alternatively, is 36/49 bigger than 45/65? The latter 9/13, or 36/52, so we can see 36/49 is bigger than 36/52

16

u/rustierpete 1d ago

I think that there is a missing variable in you calculation. If we assume that more middle is a desirable pizza. And that 0.75“ from the edge is crust.

Pizza 1 has

~ 2pi6(65/360)0.75 =5.1 square inches of crust

And Pizza 2 has

~ 2pi7(45/360)0.75 =4.1 square inches of crust

This makes pizza 2 better value for money, but still not as good as pizza 1.

Please excuse my heinous approximation and my apologies to crust lovers everywhere.

6

u/Lomega18 1d ago

I love all parts of my pizza the same.

But if OP does not like crust, then yeah, you'd be right i guess ^^

4

u/st1ckmanz 1d ago

you, my friend, are a scholar and a gentleman.

1

u/CapitalNatureSmoke 1d ago

We’re also not accounting for the better pepperoni coverage on the 7” pizza.

Plus, based on the pictures, they seem to be made from different pepperonis. So there may be a qualitative difference as well.

4

u/MediaSmurf 1d ago

Should you take into account how big the crust is? Usually there is no topping on the crust. So there should be a chance that the 7 inch pizza has more topping, depending on the crust size.

2

u/YoungMaleficent9068 1d ago

Did all the work and then didn't tell us how much $/squareinch

2

u/[deleted] 1d ago

How much of that is crust, though?

1

u/zerpa 1d ago

In practice, the 6" pizza will be 60° (6 slices) not 65° (5.5 slices). In that case, it is slightly smaller than the 7" slice. Accounting for discarded crust, it is even worse.

1

u/Res_Novae17 1d ago

Honestly, I don't mean to be a snob, but this is ninth grade math. This sub used to be about calculus and shit.

1

u/Silly_Illustrator_56 1d ago

But on which slice do you have a better crust to filling ratio?

1

u/SamTheGill42 1d ago

Then the real question: taking the crust into consideration, which one has more "pizza with stuff on it"?

Knowing the crust width isn't given, I guess the easiest would be to make it an optimization problem. "At which width of crust does the 7 inch one become better than the 6 inch one?" And I could even see another variable being added: the ratio at which someone likes the crust compared to the rest of the pizza.

1

u/adognameddanzig 1d ago

Did you account for how much of the surface area is crust?

1

u/Usta_ 1d ago

But how much of it is actual pizza and not crust?

1

u/cybrcld 1d ago

But wider arc also mean more crust! We didn’t take that into account. What even about pizza thickness??? Pepperonis look bigger on the 7” too

1

u/joe102938 1d ago

Counterpoint: 6 inch is more crust and smaller pepperonis.

1

u/ThatOneRandomGoose 1d ago

How long did it take you to calculate that? I now want to find out if it's actually worth doing the time to do the math rather then accidently spending a few extra cents

1

u/DarthSeatb3lt 11h ago

More of the 6" is crust though

118

u/A1_Killer 1d ago

65/360 * pi * 62 = 20.41 inch2

45/360 * pi * 72 = 19.24 inch2

Slice on the left has more pizza and is cheaper so is the better deal.

15

u/meIpno 1d ago

I know you just followed the given numbers but is not to far fetch to assume the 6 inch pizza is actually 60deg (6 slices per pizza instead of 5.5 at 65deg)

4

u/LeoXCV 1d ago

The .5 leftover is the underpaid worker tax

2

u/meIpno 1d ago

Man if I had to cut pizza at a 65deg angle I'd go mad

1

u/Legitimate_Dust_3853 1d ago

Most likely not perfectly cut.

1

u/Intergalactyc 7h ago

Actually, I just measured it, left slice is actually 45 degrees and right is 36! Don't know why the given numbers are so far off but they are.

2

u/factorion-bot 7h ago

The factorial of 36 is 371993326789901217467999448150835200000000

This action was performed by a bot. Please DM me if you have any questions.

1

u/Intergalactyc 7h ago

Good bot 😍

3

u/Double_A_92 1d ago

Realistically it will be 60° though.

30

u/IkkeTM 1d ago edited 1d ago

360/65 = 5.53 Why would you cut Pizza in 5 slices of 65 degrees and then throw away half a slice? 45 degre makes sense, 60 degrees makes sense, the staff wont like it, but 72 degree divides up a pizza. But why 65 degrees?

We are not being told the whole story here.

9

u/EverynLightbringer 1d ago

It’s entirely plausible that this was cut by hand without a guide and this particular slice ended up being 65 degrees. In fact you could easily have 2 slices at 65 degrees, 2 at 55 degrees, and 2 at 60 degrees, from three cuts, if one of those cuts is off by 5 degrees.

0

u/nhorvath 1d ago

or 2 cuts off by 2.5

2

u/Intergalactyc 7h ago

Given numbers are wrong - I measured them, they're 45 and 36 degrees as imaged, not 65/45 as given! And this turns out to split the pizza into 8 and 10 slices respectively.

2

u/Cacapipitantan 1d ago

Right? What are they doing with the remaining 35 degrees? This shouldn't be bothering me this much

2

u/nhorvath 1d ago

5 slices to sell 1 for the kitchen /s

1

u/HighArctic 1d ago

thats the cooks cut

1

u/Nuker-79 1d ago

Equal opportunities in the workplace has a lot to answer for

13

u/Reasonable_Blood6959 1d ago

Area of a sector of a circle = (theta/360) x Pi x r2

Pizza 1. Area = (65/360) x pi x 36

Pizza 2. Area = (45/360) x pi x 49

Pizza 1 Area = 20.4 square inches

Pizza 2 Area = 19.2 square inches

Pizza 1 cost = $1.50

Pizza 2 cost = $1.70

Pizza 1 = 7.35 cents/square inch

Pizza 2 = 8.85 cents/square inch.

Pizza 1 is the better deal.

1

u/Rodolpho991 1d ago

We don't know if it really is a sector of a circle. We don't know if the pizza was cut through the middle

6

u/jippiedoe 1d ago

If you're only comparing these two, and are not interested in the actual surface area or price per surface area, I find it easier to just ignore the pi and 1/360 factors:

1.5/(36*65) < 1.7/(49*45), the $1.70 pizza is more expensive per surface area.

1.7/(49*45)/(1.5/(36*65))=1.2: the $1.70 pizza costs you 20% more money per cm^2 (or square inch, or any other unit of surface area).

2

u/wndtrbn 1d ago

This should be higher up, but you don't even have to calculate in the prices. When you calculate 65 * 36 and 45 * 49, and you see 65 * 36 is more area for a lower price, then that's the answer.

7

u/jimwa_1 1d ago

Pizza A is 6 inches in diameter and is ~13.61 inch2 per $1.00

Pizza B is 7 inches in diameter and is ~11.32 inch2 per $1.00

Pizza A is the better choice per $

3

u/Oxke 1d ago

Since we just want to know which one is bigger let's do the ratio:

(6²π * 65/360) / (7²π * 45/360) = 6²/7² * 65/45 = 6²/7² * 13/3² = 52/49 > 1

Hence the 6 inch slice is bigger

3

u/throwaway2024ahhh 1d ago

area of circle = pi,r^2. First slice r is 6, 2nd slice r is 7. So first one is 36pi and second one is 49pi. 36pi * 65/360 vs 49pi * 45/360. 2340/1.5 vs 2205/1.7.

pi and /360 cancels out on each side so 1560 vs 1297 per dollar of pizza? 1560/1297 seems that pizza A has 20% more value/cost ratio compared to pizza B. Is my math correct?

3

u/Previous_Life7611 1d ago

The left one has an area of 20.42 sqin. Taking the price into account, we get 7.3 cents per square inch.

The one on the right has an area of 19.24 sqin and a price of 8.8 cents per square inch.

The slice on the left is a better deal.

2

u/splendidtowels 1d ago

Using area = (1/2)(rsquared)(theta), pizza 1 is 20.4in squared and pizza 2 is 19.2in squared. Pizza 2 is smaller and for a price increase of 20 cents, pizza 2 is not worth it.

2

u/HappyKoAlA312 1d ago

Pizza a is bigger than pizza b but

Pizza A crust edge is 2pi × r × 65/360

Pizza B crust edge is 2pi × r × 45/360

So pizza A crust edge is 26/21 times bigger. Edit: for better formatting

2

u/victorolosaurus 1d ago

this is the correct way to make these problems interesting.. not plugin weird numerical values but make it dependent on the relative evaluation of crust

2

u/SR2025 1d ago edited 1d ago

What about the larger slices of pepperoni on the 7 inch slice? I'd like more pepperoni. The left has more slices, but the right has larger ones. This is gonna be tricky.

2

u/SnooDogs2336 1d ago

Well considering that the diameter is 6 inches, the radius is 3 So the area of the slice is 1.1349=5.103 sq inch For the 7 incher, its pi/8(3.5)2=4.81 sq inch So yes the 6 inch is better provided all the slices are the same size

1

u/OffPoopin 1d ago

One of the things I'm most grateful for from school lessons, was a teacher that taught me how valuable Quick Estimation Math is. Very practical. I just counted the pepperonis, assuming uniform coverage on both pies, and the pepperonis were the same diameter for both. 6" all day

1

u/Enderbyte09 1d ago

Let's first calculate for the 6inch pizza:
The slice is ~18% of the pizza. Since the pizza has a radius of 6 inches, the total area is =pi*r^2 = pi*36 = ~113 in^2. The slice occupies a total of 20.3 in^2 of pizza. Divide by 1.50 = 13.57 in^2/$

For the second pizza:
~12.5% slice * pi*49 = 19.24 in^2 = 11.32 in^2/$

The first pizza is of better value.

1

u/Dinklepuffus 19h ago

For anyone wondering if the 7” pizza has more ‘sauced’ area, the answer is it depends.

If we say the crust has a thickness x, and cancel out the factor of pi/360, then we can set up the following equation:

45(7 - x)2 = 65(6 - x)2

we can then expand/simplify into a quadratic eqution:

45(x2 - 14x + 49) = 65(x2 - 12x + 36)

452 - 630 + 2205 = 652 - 780x + 2340

20x2 - 150x + 135 = 0

4x2 - 30x + 27 = 0

and then complete the square to solve for x:

4[x2 - 7.5x] + 27 = 0

4[(x - 3.75)2 - 14.0625] + 27 = 0

4(x - 3.75)2 - 56.25 + 27 = 0

4(x - 3.75)2 - 29.25 = 0

(x - 3.75)2 = 7.3125

x = 3.75 +/- sqrt(7.3125)

x = 1.045 or 6.454 inches

we can ignore 6.454 as this is greater than the radius of the 6” pizza, so the crust would have to be just over 1” thick for the 7” slice to have more sauced area. Whether that is worth the increased cost depends on your preferences and if you like crust.

1

u/Intergalactyc 7h ago

Piggybacking on u/nzivvo 's comment, as they were one of the few that I saw that doubted the angles:

Yes, the angles given in the image are indeed incorrect! Actually measuring the angles in the image, the left is actually about 45 degrees (1/8 of the pizza) and the right 36 degrees (1/10 of the pizza).

Assuming these are "standard slices", the numbers do still work out in this case for the 6" pizza being a slightly better deal in total price per unit area, but less so than if taking the angles at face value.

1

u/Few-Yogurtcloset6208 7h ago

Without doing the math, the angle should be linear area scaling and the radius is square scaling. So 65/45 = 13/9 = 1.44, and 36/49 = 1 + 13/36, 1/36th over 1.33 so like 1.365.

So by proportion the 6inch pizza is going to be larger, and it's cheaper. My intuition is the 7in would be better deal if the prices were inverted, but it'd be close.

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u/nzivvo 1d ago

I think the other comments are a common case of blindly applying math without common sense/logic.

Its clear the angles on the photo are incorrect/misleading. You cant cut a pizza evenly into 65deg slices. I therefore believe the 6inch slice is supposed to be 60deg (6 slices per pizza). And the 7inch slice is supposed 45deg (8 slices per pizza):

60/360 * pi * 62 = 18.84 inch2

45/360 * pi * 72 = 19.24 inch2

Thats 2% more area for the 7inch.

Also, alot of people prefer to maximise the toppings and not crust. If we assume 0.5 inches of crust per pizza then the 7inch slice has an even greater proportion of toppings:

60/360 * pi * 5.52 = 15.83 inch2

45/360 * pi * 6.52 = 16.59 inch2

Thats 5% more toppings.

Either way it doesnt seem worth the 13% price hike

1

u/Thalidomidas 1d ago

65 degree slice for the 6 inch !

1

u/nzivvo 1d ago

Nope, not logical

1

u/Thalidomidas 1d ago

Perhaps they also offer a 35degree slice as part of something else !

1

u/Intergalactyc 7h ago

Actually, you are indeed correct that the angles are wrong - they turn out to be 45 and 36 degrees, respectively!!

1

u/HeroBrine0907 1d ago

You can't change the question and claim everyone else is wrong. We're asked to cmpare two slices. This is just delierate misinterpretation.

1

u/Intergalactyc 7h ago

Try actually measuring the angles of the pictured pizza slices. The angles given in the image are indeed wrong - they're actually 45 and 36 degrees. While above commenter isn't completely right they are correct to doubt the given numbers.

0

u/nzivvo 21h ago

I can. And I just did.

0

u/DefinitelyATeenager_ 1d ago

You cant cut a pizza evenly into 65deg slices

Nobody said all the slices are equal. This specific slice is 65 degrees, that's what matters. Maybe other slices have different angles, but this specific slice is what matters.

0

u/romulusnr 1d ago

The second, by about a square inch.

https://www.omnicalculator.com/math/isosceles-triangle

the angle is β and the length is leg

edit: There is of course the "arc" area outside the triangle but it's presumably insignificantly different.

0

u/CaptnSpazmo 1d ago

If this was how they taught Maths in school I wouldve paid wwawayyyyyyy more attention. This is useful real life application of maths, not like that physics and engineering mumbo jumbo