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A stack of 75 identical plastic plates f...

A stack of 75 identical plastic plates forms a column approximately `9 (7)/(8)` inches tall. At this rate, which of the following is closest to the number of plates that would be needed to form a column 20 inches tall ?

A

125

B

150

C

185

D

220

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of how many plates are needed to form a column 20 inches tall, we can follow these steps: ### Step 1: Convert the height of the column from mixed number to improper fraction. The height of the column is given as \(9 \frac{7}{8}\) inches. To convert this to an improper fraction: \[ 9 \frac{7}{8} = \frac{9 \times 8 + 7}{8} = \frac{72 + 7}{8} = \frac{79}{8} \text{ inches} \] **Hint:** To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. ### Step 2: Determine the height of one plate. We know that 75 plates stack to a height of \(\frac{79}{8}\) inches. Therefore, the height of one plate can be calculated as: \[ \text{Height of one plate} = \frac{\frac{79}{8}}{75} = \frac{79}{8 \times 75} = \frac{79}{600} \text{ inches} \] **Hint:** To find the height of one item in a group, divide the total height by the number of items. ### Step 3: Calculate the number of plates needed for a 20-inch column. Now, we want to find out how many plates are needed to reach a height of 20 inches. We can set up the equation: \[ \text{Number of plates} = \frac{20}{\text{Height of one plate}} = 20 \div \frac{79}{600} = 20 \times \frac{600}{79} \] **Hint:** To divide by a fraction, multiply by its reciprocal. ### Step 4: Simplify the calculation. Now we compute: \[ 20 \times \frac{600}{79} = \frac{12000}{79} \] ### Step 5: Perform the division. Now we need to calculate \(\frac{12000}{79}\): \[ 12000 \div 79 \approx 151.8987 \] Since we are looking for the closest whole number, we round this to 152. **Hint:** When estimating, if the decimal is .5 or higher, round up; otherwise, round down. ### Final Answer: The closest number of plates needed to form a column 20 inches tall is approximately **152 plates**.
To solve the problem of how many plates are needed to form a column 20 inches tall, we can follow these steps: ### Step 1: Convert the height of the column from mixed number to improper fraction. The height of the column is given as \(9 \frac{7}{8}\) inches. To convert this to an improper fraction: \[ 9 \frac{7}{8} = \frac{9 \times 8 + 7}{8} = \frac{72 + 7}{8} = \frac{79}{8} \text{ inches} \] ...
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