Tito and Luis..

Question

Tito and Luis are stuffed with pizza! Tito ate one-fourth of a cheese pizza. Tito ate three eights of a pepperoni pizza . Luis ate the other half of the mushroom pizza. All the pizzas were the same size. Tito says he ate more

pizza than Luis because Luis did not eat any pepperoni pizza. Luis says they each ate the same amount of pizza. Who is correct? Show all your mathematical thinking.

Answer 1

Because we talk Math, I would resort to the most stringent reading of this word problem, including the causal relationship. Both are wrong!

On the first reading of the problem, we should conclude that our calculations would come to eights!

[That's what I teach (among other things, of course): Note on the initial reading:

1. What is in question?
2. Figure out before making the calculations: In which units we are going to do "critical" calculations.

]

Given: Tito ate one-fourth of a cheese pizza. Tito ate 1/4 = 2/8.

Given: Tito ate three eights of a pepperoni pizza. Tito ate 3/8.

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Given: Luis ate (the other) half of the mushroom pizza. Luis ate 1/2 = 4/8.

[That's what I teach (among other things, of course): Note and exclude (mentally or even put in writing) Irrelevant / extraneous data (yes, it happens even on the test problems!):

1. What does NOT have any bearing on what is in question? in our case "the other" does NOT have any bearing.

]

Tito ate total of 2/8 + 3/8 = 5/8 pizza.

Luis ate total of 4/8 pizza.

Tito is wrong, as, even he ate more pizza, but NOT for the stated reason, "because Luis did not eat any pepperoni pizza". Counterexample: If Luis had ate 1/16 pepperoni pizza, he would end up eating 4/8 + 1/16 = 8/16 + 1/16 = 9/16 pizza, whereas Tito ate 10/16 pizza, still more than Luis, even if Luis ate (in this counterexample) pepperoni pizza.

Luis is wrong saying "they each ate the same amount of pizza", because 5/8 is not equal 4/8.

Answer (to question "Who is correct?" None of them is correct.

The above would be my teaching. On the Test problem expressly requesting "Show all your mathematical thinking", I would recommend to have the following.

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Question: Who is correct?

Given: Tito ate one-fourth of a cheese pizza. Tito ate 1/4 = 2/8.

Given: Tito ate three eights of a pepperoni pizza. Tito ate 3/8.

Tito ate total of 2/8 + 3/8 = 5/8 pizza

Given: Luis ate half of the mushroom pizza. Luis ate 1/2 = 4/8

Luis ate total of 4/8 pizza

Tito is wrong, as, even he ate more pizza, but NOT for the stated reason, "because Luis did not eat any pepperoni pizza". Counterexample: If Luis had also ate 1/16 a pepperoni pizza, he would end up eating 4/8 + 1/16 = 8/16 + 1/16 = 9/16 pizza, whereas Tito ate 10/16 pizza, still more than Luis, even if Luis had ate (in this counterexample) pepperoni pizza.

Luis is wrong saying "they each ate the same amount of pizza", because 5/8 is not equal 4/8.

Answer None of them is correct.

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Answer 2

Tito ate 1/4 of cheese

Luis ate "the other half" it 1/4 = 1/2, then the "other half" = 1/4 too

"other half" is very ambiguous

then Tito ate 3/8 of a pepperoni of same size. 3/8+1/4 = 5/8 of pizza> 1/4 any ways you slice it

Unless Luis eating the "other half" means the rest of the cheese pizza = 3/4

then 3/8+1/4 =5/8 < 3/4 and Luis is right

Answer 3

Well, this is a fun problem!

Let's start with Tito. He ate 1/4 of one pizza and then ate 3/8 of another. Getting a common denominator, that means he ate 2/8 + 3/8, which equals 5/8.

Luis ate 1/2 of a pizza. To compare the two, we again need a common denominator. Luis ate 4/8.

Tito's 5/8 > Luis 4/8, so Tito ate more.

Answer 4

Tito: (1/4) + (3/8) = 5/8

Luis: 1/2 = 4/8