Sure, let's go through each part of the question step by step.
### a. Find the missing values in the two tables above.
Loren's Table:
Given:
- Hours: 2, 4, 6, 8, 10, 12, 14, 16, 18
- Dollars: 18, 36, 54, 72, 90, 108, ?, ?, 162
To find Loren's rate of pay:
- He makes [tex]$18 for 2 hours, so he makes $[/tex]18 / 2 = [tex]$9 per hour.
Calculate the missing values:
- For 14 hours: 14 hours * $[/tex]9/hour = [tex]$126
- For 16 hours: 16 hours * $[/tex]9/hour = [tex]$144
So, Loren's complete table:
- Dollars: 18, 36, 54, 72, 90, 108, 126, 144, 162
Julie's Table:
Given:
- Hours: 3, 6, 9, 12, 15, 18, 21, 24, 27
- Dollars: 36, ?, 108, 144, 180, 216, ?, 288, 324
To find Julie's rate of pay:
- She makes $[/tex]36 for 3 hours, so she makes [tex]$36 / 3 = $[/tex]12 per hour.
Calculate the missing values:
- For 6 hours: 6 hours [tex]$12/hour = $[/tex]72
- For 21 hours: 21 hours [tex]$12/hour = $[/tex]252
So, Julie's complete table:
- Dollars: 36, 72, 108, 144, 180, 216, 252, 288, 324
### b. Who makes more per hour? Justify your answer.
Julie makes more per hour. We found that Loren makes [tex]$9 per hour and Julie makes $[/tex]12 per hour. Since [tex]$12 is greater than $[/tex]9, Julie makes more per hour.
### c. Write how much Julie makes as a rate. What is the unit rate?
Julie makes [tex]$12 per hour. This rate means that for every hour Julie works, she earns $[/tex]12.
### d. How much money would Julie earn for working 16 hours?
To find out how much Julie would earn for working 16 hours, we use her hourly rate of [tex]$12 per hour:
- 16 hours * $[/tex]12/hour = [tex]$192
So, Julie would earn $[/tex]192 for working 16 hours.
### e. What is the ratio between how much Loren makes per hour and how much Julie makes per hour?
The ratio of Loren's rate to Julie's rate:
- Loren's rate: [tex]$9 per hour
- Julie's rate: $[/tex]12 per hour
The ratio:
- [tex]$9 / $[/tex]12 = 0.75
So, the ratio between how much Loren makes per hour and how much Julie makes per hour is 0.75.
### f. Julie works [tex]\(\frac{1}{12}\)[/tex] hours/dollar. Write a one or two-sentence explanation of what this rate means. Use this rate to find how long it takes for Julie to earn [tex]$\$[/tex] 228[tex]$.
This rate means that for every dollar Julie earns, she works \(\frac{1}{12}\) hour. To find out how long it takes for Julie to earn $[/tex]228:
- Time = [tex]$228 * \(\frac{1}{12}\) hours/dollar
- Time = 19 hours
So, it takes Julie 19 hours to earn $[/tex]228.
By following these steps, we've addressed each part of the problem and provided the necessary calculations and explanations.
