Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Confidence Intervals
When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calcul…
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**Mathematical Problem on Proportions: Pâté Order for Events** **Problem Statement:** A couple ordered 70 ounces of pâté for their engagement party of 45 people. The pâté was such a hit that the couple has decided to serve it again at their wedding reception. How many ounces of pâté should they order for 315 people? **Solution Explanation:** 1. **Identify the Proportion:** - At the engagement party, 70 ounces of pâté were sufficient for 45 people. 2. **Set Up the Proportion:** To find out the amount required for 315 people, we set up the following proportion: \[ \frac{70 \text{ ounces}}{45 \text{ people}} = \frac{x \text{ ounces}}{315 \text{ people}} \] 3. **Solve for x:** - Cross-multiply and solve for \( x \): \[ 70 \, \text{ounces} \times 315 \, \text{people} = 45 \, \text{people} \times x \, \text{ounces} \] \[ 22050 = 45x \] \[ x = \frac{22050}{45} \] \[ x = 490 \] 4. **Conclusion:** The couple should order 490 ounces of pâté for 315 people to ensure the same proportion of pâté per person as their engagement party. This method of solving the problem utilizes basic proportion concepts in mathematics, which can be applied in various real-world scenarios.
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Transcribed Image Text:**Mathematical Problem on Proportions: Pâté Order for Events** **Problem Statement:** A couple ordered 70 ounces of pâté for their engagement party of 45 people. The pâté was such a hit that the couple has decided to serve it again at their wedding reception. How many ounces of pâté should they order for 315 people? **Solution Explanation:** 1. **Identify the Proportion:** - At the engagement party, 70 ounces of pâté were sufficient for 45 people. 2. **Set Up the Proportion:** To find out the amount required for 315 people, we set up the following proportion: \[ \frac{70 \text{ ounces}}{45 \text{ people}} = \frac{x \text{ ounces}}{315 \text{ people}} \] 3. **Solve for x:** - Cross-multiply and solve for \( x \): \[ 70 \, \text{ounces} \times 315 \, \text{people} = 45 \, \text{people} \times x \, \text{ounces} \] \[ 22050 = 45x \] \[ x = \frac{22050}{45} \] \[ x = 490 \] 4. **Conclusion:** The couple should order 490 ounces of pâté for 315 people to ensure the same proportion of pâté per person as their engagement party. This method of solving the problem utilizes basic proportion concepts in mathematics, which can be applied in various real-world scenarios.
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