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Exactly 52% of the marbles in a jar are ...

Exactly `52%` of the marbles in a jar are red. Which of the following could be the total number of marbles in the jar?

A

20

B

21

C

25

D

28

Text Solution

AI Generated Solution

The correct Answer is:
To determine which of the given options could be the total number of marbles in the jar, we need to calculate the number of red marbles for each option based on the fact that 52% of the marbles are red. The number of red marbles must be an integer, so we will check each option one by one. ### Step-by-Step Solution: 1. **Option 1: 20 marbles** - Calculate the number of red marbles: \[ \text{Number of red marbles} = 20 \times \frac{52}{100} = 20 \times 0.52 = 10.4 \] - Since 10.4 is not an integer, **20 marbles cannot be the total.** 2. **Option 2: 21 marbles** - Calculate the number of red marbles: \[ \text{Number of red marbles} = 21 \times \frac{52}{100} = 21 \times 0.52 = 10.92 \] - Since 10.92 is not an integer, **21 marbles cannot be the total.** 3. **Option 3: 25 marbles** - Calculate the number of red marbles: \[ \text{Number of red marbles} = 25 \times \frac{52}{100} = 25 \times 0.52 = 13 \] - Since 13 is an integer, **25 marbles could be the total.** 4. **Option 4: 28 marbles** - Calculate the number of red marbles: \[ \text{Number of red marbles} = 28 \times \frac{52}{100} = 28 \times 0.52 = 14.56 \] - Since 14.56 is not an integer, **28 marbles cannot be the total.** ### Conclusion: After evaluating all options, the only possible total number of marbles in the jar is **25**.
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