QuestionHow many friends can you invite so that 24 slices of pizza and 90 tokens are evenly shared? How much does each get?

Studdy Solution

STEP 1

Assumptions1. The total number of pizza slices is24. . The total number of tokens is90.
3. The slices of pizza and tokens must be equally split between you and your friends.
4. There should be no pizza slices or tokens left over.

STEP 2

We need to find the greatest common divisor (GCD) of the total number of pizza slices and the total number of tokens. The GCD is the largest number that divides both numbers without leaving a remainder. This will give us the greatest number of friends we can invite such that the pizza slices and tokens can be equally split with none left over.
$GCD = GCD(24,90)$

STEP 3

First, we find the GCD of24 and90.
$GCD(24,90) =6$

STEP 4

Now that we have the GCD, we can find the number of friends we can invite. Since the pizza slices and tokens will be equally split between you and your friends, we subtract1 from the GCD (for yourself).
$Number\, of\, friends = GCD -1$

STEP 5

Plug in the value for the GCD to calculate the number of friends.
$Number\, of\, friends = -1$

STEP 6

Calculate the number of friends.
$Number\, of\, friends =6 -1 =5$

STEP 7

Now that we have the number of friends, we can find the number of pizza slices each person will receive. This can be done by dividing the total number of pizza slices by the total number of people (you and your friends).
$Pizza\, slices\, per\, person = Total\, pizza\, slices / Total\, people$

STEP 8

Plug in the values for the total number of pizza slices and the total number of people to calculate the pizza slices per person.
$Pizza\, slices\, per\, person =24 / (5 +1)$

STEP 9

Calculate the number of pizza slices each person will receive.
$Pizza\, slices\, per\, person =24 /6 =4$

STEP 10

Similarly, we can find the number of tokens each person will receive. This can be done by dividing the total number of tokens by the total number of people.
$Tokens\, per\, person = Total\, tokens / Total\, people$

STEP 11

Plug in the values for the total number of tokens and the total number of people to calculate the tokens per person.
$Tokens\, per\, person =90 / (5 +)$

STEP 12

Calculate the number of tokens each person will receive.
$Tokens\, per\, person =90 /6 =15$ You can invite5 friends to the arcade. Each person will receive4 slices of pizza and15 tokens.

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