Question

Miranda has a box with 160 coins consisting of quarters and dimes. She randomly selects 20 coins from the box. 8 of the coins are dimes and 12 are quarters. Miranda puts the coins back in the box.
Based on Miranda's sample, estimate the number of each coin in the box.
Enter a number in each empty box of the table.

Sample
Total
Quarters
12


Dimes
8


Total
20
160

Calculator

Answer 1

To estimate the number of quarters and dimes in the box based on Miranda's sample, we can use the proportion of coins in her sample to estimate the total amounts in the box.

From the sample:
- Dimes selected: 8
- Quarters selected: 12
- Total coins selected: 20

From this sample, we can calculate the proportion of each type of coin:

1. **Proportion of Dimes**:
\[
\text{Proportion of dimes} = \frac{\text{dimes sampled}}{\text{total sampled}} = \frac{8}{20} = 0.4
\]

2. **Proportion of Quarters**:
\[
\text{Proportion of quarters} = \frac{\text{quarters sampled}}{\text{total sampled}} = \frac{12}{20} = 0.6
\]

Now, we can use these proportions to estimate the total number of dimes and quarters in the box of 160 coins.

3. **Estimated Number of Dimes**:
\[
\text{Estimated number of dimes} = \text{Total coins} \times \text{Proportion of dimes} = 160 \times 0.4 = 64
\]

4. **Estimated Number of Quarters**:
\[
\text{Estimated number of quarters} = \text{Total coins} \times \text{Proportion of quarters} = 160 \times 0.6 = 96
\]

Now we can fill out the table with these estimates:

| Total | Dimes | Quarters |
|-------|-------|----------|
| 160 | 64 | 96 |
| Total | 20 | 160 |

Thus, based on Miranda's sample:
- Estimated number of dimes = **64**
- Estimated number of quarters = **96**