Subjects algebra

Percent Problems Dcc50E

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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.