Estimate the answer by rounding each number to one nonzero digit first, then perform the actual calculation. Lucy eams \( \$ 7.50 \) per hour at a local restaurant. She eams time and a half for each hour she works on a holiday. Lucy worked six hours each day for four days, then worked five hours on a holiday. How much did she eam for that week? Find the estimale value. She eamed about \( \$ 272 \) for that week. (Round to the nearest whole number as needed.) Find the exad value. She eamed \( \$ \square \) for that week. (Round to the nearest hundredth as needed.)

To estimate Lucy's earnings, we first round her hourly wage and the number of hours she worked. 1. **Hourly Wage**: - \( \$7.50 \) rounds to \( \$8.00 \). 2. **Regular Hours Worked**: - Lucy worked 6 hours each day for 4 days: - \( 6 \times 4 = 24 \) hours. - Rounding \( 24 \) to one nonzero digit gives us \( 30 \) (since we round to the nearest ten). 3. **Holiday Hours Worked**: - Lucy worked 5 hours on a holiday, which rounds to \( 5 \). 4. **Total Estimated Hours**: - Estimated total hours = \( 30 + 5 = 35 \). 5. **Estimated Earnings**: - Regular earnings for 30 hours at \( \$8.00 \) per hour: - \( 30 \times 8 = 240 \). - Holiday earnings for 5 hours at time and a half (\( 1.5 \times 8 = 12 \)): - \( 5 \times 12 = 60 \). - Total estimated earnings = \( 240 + 60 = 300 \). So, the estimated value is about \( \$300 \). Now, let's calculate the exact value. 1. **Regular Hours Worked**: - Lucy worked 6 hours each day for 4 days: - \( 6 \times 4 = 24 \) hours. 2. **Holiday Hours Worked**: - Lucy worked 5 hours on a holiday. 3. **Total Hours**: - Total hours = \( 24 + 5 = 29 \) hours. 4. **Regular Earnings**: - Regular earnings for 24 hours at \( \$7.50 \) per hour: - \( 24 \times 7.50 = 180 \). 5. **Holiday Earnings**: - Holiday earnings for 5 hours at time and a half: - Time and a half = \( 1.5 \times 7.50 = 11.25 \). - Holiday earnings = \( 5 \times 11.25 = 56.25 \). 6. **Total Earnings**: - Total earnings = \( 180 + 56.25 = 236.25 \). Thus, the exact value is \( \$236.25 \). In summary: - Estimated value: \( \$300 \) - Exact value: \( \$236.25 \)