To solve the problems involving
Percentage (P),
Base (B), and
Rate (R), we use the relationship:
\[
P = B \times R
\]
Where:
- \( P \) is the Percentage,
- \( B \) is the Base,
- \( R \) is the Rate (expressed as a decimal).
Step-by-Step Solutions:
#### 1. \( R = 18\% \), \( B = 27 \), \( P = ? \)
- Convert \( R \) to a decimal: \( R = 0.18 \)
- Use the formula: \( P = B \times R \)
- \( P = 27 \times 0.18 = 4.86 \)
Answer: \( P = 4.86 \)
#### 2. \( B = 50 \), \( P = 25 \), \( R = ? \)
- Use the formula: \( R = \frac{P}{B} \)
- \( R = \frac{25}{50} = 0.5 \)
- Convert \( R \) back to a percentage: \( R = 50\% \)
Answer: \( R = 50\% \)
#### 3. \( P = 2,450 \), \( R = 20\% \), \( B = ? \)
- Convert \( R \) to a decimal: \( R = 0.20 \)
- Use the formula: \( B = \frac{P}{R} \)
- \( B = \frac{2,450}{0.20} = 12,250 \)
Answer: \( B = 12,250 \)
#### 4. \( R = 3\% \), \( B = 345 \), \( P = ? \)
- Convert \( R \) to a decimal: \( R = 0.03 \)
- Use the formula: \( P = B \times R \)
- \( P = 345 \times 0.03 = 10.35 \)
Answer: \( P = 10.35 \)
#### 5. \( B = 80 \), \( P = 20 \), \( R = ? \)
- Use the formula: \( R = \frac{P}{B} \)
- \( R = \frac{20}{80} = 0.25 \)
- Convert \( R \) back to a percentage: \( R = 25\% \)
Answer: \( R = 25\% \)
#### 6. \( R = 25\% \), \( P = 8 \), \( B = ? \)
- Convert \( R \) to a decimal: \( R = 0.25 \)
- Use the formula: \( B = \frac{P}{R} \)
- \( B = \frac{8}{0.25} = 32 \)
Answer: \( B = 32 \)
#### 7. \( P = 18 \), \( B = 90 \), \( R = ? \)
- Use the formula: \( R = \frac{P}{B} \)
- \( R = \frac{18}{90} = 0.20 \)
- Convert \( R \) back to a percentage: \( R = 20\% \)
Answer: \( R = 20\% \)
#### 8. \( B = 22 \), \( R = 50\% \), \( P = ? \)
- Convert \( R \) to a decimal: \( R = 0.50 \)
- Use the formula: \( P = B \times R \)
- \( P = 22 \times 0.50 = 11 \)
Answer: \( P = 11 \)
#### 9. \( R = 40\% \), \( B = 200 \), \( P = ? \)
- Convert \( R \) to a decimal: \( R = 0.40 \)
- Use the formula: \( P = B \times R \)
- \( P = 200 \times 0.40 = 80 \)
Answer: \( P = 80 \)
#### 10. \( R = 80\% \), \( P = 16 \), \( B = ? \)
- Convert \( R \) to a decimal: \( R = 0.80 \)
- Use the formula: \( B = \frac{P}{R} \)
- \( B = \frac{16}{0.80} = 20 \)
Answer: \( B = 20 \)
Final Answers:
\[
\boxed{
\begin{array}{lll}
1. & P = 4.86 \\
2. & R = 50\% \\
3. & B = 12,250 \\
4. & P = 10.35 \\
5. & R = 25\% \\
6. & B = 32 \\
7. & R = 20\% \\
8. & P = 11 \\
9. & P = 80 \\
10. & B = 20 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of rate worksheet grade 6.
