Answer:

Step-by-step explanation:

To find out how many plates can be used to arrange 90 cupcakes with an equal number of cupcakes on each plate, you can follow these steps:

Determine the number of cupcakes you want on each plate. Let's call this number "C."

Divide the total number of cupcakes (90) by the number of cupcakes per plate (C):

Number of plates = Total number of cupcakes / Number of cupcakes per plate

Number of plates = 90 / C

To have an equal number of cupcakes on each plate, you'll need to find a value of "C" that evenly divides 90 without leaving a remainder.

List the factors of 90 to see which values of C will work:

Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

To arrange the cupcakes with an equal number on each plate, you can choose any of the factors of 90 as the number of cupcakes per plate (C).

So, the number of plates will vary depending on the number of cupcakes on each plate. You can use any of the factors of 90, and the number of plates required will be the result of the division 90 / C, where C is the number of cupcakes per plate.

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To find out the number of plates that can be used for arranging the cupcakes, we need to find a number that can divide 90 evenly. Here are the steps:

1. Start with the smallest possible number of plates, which is 1.

2. Divide 90 by 1 to see if it divides evenly. In this case, 90 ÷ 1 = 90.

3. Check if the result is a whole number. Since 90 is divisible by 1, we move on to the next number.

4. Increase the number of plates to 2.

5. Divide 90 by 2 to see if it divides evenly. In this case, 90 ÷ 2 = 45.

6. Check if the result is a whole number. Since 45 is divisible by 2, we move on to the next number.

7. Repeat steps 4-6, increasing the number of plates each time, until we find a number that does not divide evenly into 90.

8. The last number of plates that divided evenly into 90 is the answer.

Let's go through the steps:

1 plate: 90 ÷ 1 = 90 (whole number)

2 plates: 90 ÷ 2 = 45 (whole number)

3 plates: 90 ÷ 3 = 30 (whole number)

4 plates: 90 ÷ 4 = 22.5 (not a whole number)

Therefore, the last number of plates that divided evenly into 90 is 3.

So, the correct answer is c) 11 plates.