To determine how much money Shawn received from their landscaping project, we need to follow a sequence of steps that include calculating total hours worked, the amount saved, and the distribution of earnings.
### Step-by-Step Solution:
1. Calculate the total hours worked by each individual:
- Edgar worked [tex]\(17 \frac{1}{4}\)[/tex] hours, which is equivalent to 17.25 hours.
- Kelly worked [tex]\(18 \frac{1}{4}\)[/tex] hours, which is equivalent to 18.25 hours.
- Shawn worked [tex]\(14 \frac{1}{2}\)[/tex] hours, which is equivalent to 14.5 hours.
2. Sum the total hours worked:
[tex]\[
\text{Total hours worked} = 17.25 + 18.25 + 14.5 = 50.0 \text{ hours}
\][/tex]
3. Determine the total earnings:
[tex]\[
\text{Total earnings} = \$850
\][/tex]
4. Calculate the 15% amount put into the joint savings account:
[tex]\[
\text{Savings amount} = 0.15 \times 850 = \$127.5
\][/tex]
5. Find out the remaining amount after saving:
[tex]\[
\text{Remaining earnings} = 850 - 127.5 = \$722.5
\][/tex]
6. Distribute the remaining amount based on the hours worked:
Since we need to distribute [tex]\( \$722.5 \)[/tex] proportionally to the hours worked, we find each person's share as follows:
- First, calculate the proportion of hours Shawn worked relative to the total hours.
[tex]\[
\text{Shawn's hours proportion} = \frac{14.5}{50.0}
\][/tex]
- Multiply the proportion by the remaining earnings to find out Shawn’s share.
[tex]\[
\text{Shawn's share} = \left( \frac{14.5}{50.0} \right) \times 722.5 \approx 209.525
\][/tex]
Therefore, Shawn received approximately [tex]\( \$209.525 \)[/tex].
