Question

Zahra gave out a survey to some students in her school about their favorite color. Students could choose between purple and red. 187 of those surveyed said their favorite color was purple. 45, percent45% of the students surveyed said their favorite color was red. How many students were surveyed in total?

Answer 1

Let the total number of students surveyed be \( x \).

According to the information given:
- The number of students who chose purple is 187.
- The percentage of students who chose red is 45%, which can also be expressed mathematically as \( 0.45x \).

Since the students could only choose between purple and red, we can express this as:
\[
\text{Number of students who chose purple} + \text{Number of students who chose red} = \text{Total students surveyed}
\]
This translates to the equation:
\[
187 + 0.45x = x
\]

Now, we can rearrange this equation to isolate \( x \). Subtract \( 0.45x \) from both sides:
\[
187 = x - 0.45x
\]
\[
187 = 0.55x
\]

Next, to find \( x \), divide both sides by 0.55:
\[
x = \frac{187}{0.55}
\]

Calculating the right-hand side:
\[
x = 340
\]

Thus, the total number of students surveyed is \( \boxed{340} \).

**Verification:**
1. The number of students who chose red:
\[
0.45 \times 340 = 153
\]
2. Adding both results:
\[
187 + 153 = 340
\]

This confirms that our solution is correct.