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3 years ago

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You are setting out snacks for some friends to come over. You have 18 crackers and 12 slices of cheese. If you want each plate t

o be identical, with no food left over, what is the greatest number of plates you can prepare? How many crackers will be on each plate? How many slices of cheese will be on each plate?

1 answer:

Alex Ar [27]3 years ago

7 0

The concept of greatest common factor is used to solve this question. Then, we use it to find the number of crackers and slices of cheese, and the answer is:

The greatest number of plates you can prepare is 6.
Each plate will have 3 crackers.
Each plate will have 2 slices of cheese.

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To find the greatest number of plates, you need to find the greatest common factor between 12 and 18.

Thus, factoring them, always by the same number:

12 - 18|2

6 - 9|3

2 - 3

The greatest common factor is 2x3 = 6, which means that the greatest number of plates you can prepare is 6.

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18 crackers, so each plate has 18/6 = 3 crackers.

12 slices of cheese, so each plate has 12/6 = 2 slices of cheese.

A similar question is given at brainly.com/question/18454593

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4 years ago

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e) 2

Step-by-step explanation:

We use a Venn Diagram to solve this question.

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A are the students who like Mozart.

B are the students who like Beethoven

C are the students who like Haydn.

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$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

In which a are those who only like Mozart, $(A \cap B)$ are those who like Mozart and Beethoven, $(A \cap C)$ are those who like Mozart and Haydn and $(A \cap B \cap C)$ are those who like all three of them.

By the same logic, we have that:

$B = b + (A \cap B) + (B \cap C) + (A \cap B \cap C)$

$C = c + (B \cap C) + (A \cap C) + (A \cap B \cap C)$

We start finding these values from the intersection:

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This means that:

$(B \cap C) + (A \cap B \cap C) = 14$

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This means that:

$(A \cap C) + (A \cap B \cap C) = 21$

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This means that:

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$A \cap B = 6$

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$31 = c + 6 + 13 + 8$

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This means that $B = 36$

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b. exactly one of these composers?

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d. like Beethoven and Haydn, but not Beethoven?

I will use not Mozart.

So $B \cap C = 6$

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e. like none of these composers?

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