1. **Problem:** Li rode her bike 25% of the way to school, which equals 5 blocks. We need to find the total number of blocks from Li's home to school.
2. **Formula:** Use the proportion \( \frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100} \).
3. **Set up the proportion:** \( \frac{25}{100} = \frac{5}{x} \), where \(x\) is the total blocks.
4. **Solve for \(x\):**
$$
\frac{25}{100} = \frac{5}{x}
$$
Cross multiply:
$$
25 \times x = 100 \times 5
$$
$$
25x = 500
$$
Divide both sides by 25:
$$
\cancel{25}x = \frac{500}{\cancel{25}}
$$
$$
x = 20
$$
5. **Answer:** Li lives 20 blocks from school.
2. **Problem:** Bob brought 40% of the collected canned goods to the food pantry, which equals 160 cans. Find the total number of cans collected.
3. **Set up the proportion:** \( \frac{40}{100} = \frac{160}{x} \), where \(x\) is the total cans.
4. **Solve for \(x\):**
$$
\frac{40}{100} = \frac{160}{x}
$$
Cross multiply:
$$
40x = 100 \times 160
$$
$$
40x = 16000
$$
Divide both sides by 40:
$$
\cancel{40}x = \frac{16000}{\cancel{40}}
$$
$$
x = 400
$$
5. **Answer:** 400 cans were collected in total.
3. **Problem:** Sid memorized 60% of his lines, which equals 60 lines. Find the total number of lines in Sid's part.
4. **Set up the proportion:** \( \frac{60}{100} = \frac{60}{x} \), where \(x\) is the total lines.
5. **Solve for \(x\):**
$$
\frac{60}{100} = \frac{60}{x}
$$
Cross multiply:
$$
60x = 100 \times 60
$$
$$
60x = 6000
$$
Divide both sides by 60:
$$
\cancel{60}x = \frac{6000}{\cancel{60}}
$$
$$
x = 100
$$
6. **Answer:** Sid's part in the play is 100 lines long.
Percent Problems Dcc50E
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.