Question

Allie and Sam are ophthalmologists. Allie found that​ 40% of the 170 patients she saw in a week were​ near-sighted. Sam found that​ 25% of the 236 patients he saw in a week were​ near-sighted.
a. How many of the patients Allie saw were​ near-sighted?
b. How many of the patients Sam saw were​ near-sighted?
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Part 1
a. Find the number of​ near-sighted patients that Allie saw.
Allie saw
  
enter your response here ​near-sighted patients.

Answer 1

To find the number of near-sighted patients that Allie saw, we can use the percentage of near-sighted patients and the total number of patients she saw.

Allie's calculations:
- Total patients = 170
- Percentage of near-sighted patients = 40%

The number of near-sighted patients can be calculated as follows:
\[
\text{Number of near-sighted patients} = \text{Total patients} \times \left( \frac{\text{Percentage of near-sighted patients}}{100} \right)
\]
\[
\text{Number of near-sighted patients} = 170 \times \left( \frac{40}{100} \right) = 170 \times 0.4 = 68
\]

Thus, Allie saw **68 near-sighted patients**.

---

Now for Sam:

Sam's calculations:
- Total patients = 236
- Percentage of near-sighted patients = 25%

The number of near-sighted patients can be calculated similarly:
\[
\text{Number of near-sighted patients} = \text{Total patients} \times \left( \frac{\text{Percentage of near-sighted patients}}{100} \right)
\]
\[
\text{Number of near-sighted patients} = 236 \times \left( \frac{25}{100} \right) = 236 \times 0.25 = 59
\]

Thus, Sam saw **59 near-sighted patients**.