Question

Tito and Luis are stuffed with pizza! Tito ate one-fourth of a cheese pizza. Tito ate three-eighths of a pepperoni pizza. Tito ate one-half of a mushroom pizza. Luis ate five-eighths of a cheese 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? Explain how you got the answer.

Answer 1

Luis is correct.

Explanation:

We see that,

Tito ate
`(1)/(4)` of cheese pizza,
`(3)/(8)` of pepperoni pizza and
`(1)/(2)` of the mushroom pizza.

So, in total Tito ate =
`(1)/(4) +(3)/(8) +(1)/(2)` =
`(9)/(8)` parts of the three pizza's.

Further, Luis ate
`(5)/(8)` of cheese pizza and
`(1)/(2)` of the mushroom pizza.

So, in total Luis ate =
`(5)/(8) +(1)/(2)` =
`(9)/(8)` parts of the three pizza's.

Therefore, we can that both Tito and Luis ate
`(9)/(8)` part of the pizza.

Hence, Luis is correct that they both ate the same amount of the pizza.

Answer 2

Answer: Tito is correct.

Explanation:

According to the question,

Total part of pizza = 1 part of cheese pizza + 1 part of mushroom pizza + 1 part of pepperoni pizza = 3 part of a pizza

Part of pizza is eaten by Tito =
`(1)/(4) + (3)/(8) + (1)/(2)=(13)/(8)`

Part of pizza is eaten by Luis =
`(5)/(8) + (1)/(2) = (9)/(8)`

Since,
`(13)/(8)` part of 3 =
`(39)/(8)`

And,
`(9)/(8)` part of 3 =
`(27)/(8)`

But,
`(39)/(8)` >
`(27)/(8)`

⇒ Tito ate more part of pizza than Luis.

If Tito did not eat pepperoni pizza then his part would be
`(3)/(4)` which is less than that of Luis.

Therefore, Tito ate more pizza than that of Luis because he ate pepperoni pizza.

Thus, Tito is correct.