Question
Landscaping services from two companies, Yard Oasis and Sand n’ Stone, differ by total cost.
The total cost of landscaping services from Yard Oasis includes a one-time 168
fee for scheduling services in addition to an hourly rate of 44
per hour of service.
The total cost of landscaping services from Sand n’ Stone only includes an hourly rate of service that is 25%
more than the hourly rate of Yard Oasis.
If a homeowner hires Yard Oasis and Sand n’ Stone to complete the same number of hours of landscaping services, x
, and the homeowner’s combined cost for services from both companies is 1,554
, which statements are true?
Select ALL that apply.
The total cost of landscaping services from Yard Oasis includes a one-time 168
fee for scheduling services in addition to an hourly rate of 44
per hour of service.
The total cost of landscaping services from Sand n’ Stone only includes an hourly rate of service that is 25%
more than the hourly rate of Yard Oasis.
If a homeowner hires Yard Oasis and Sand n’ Stone to complete the same number of hours of landscaping services, x
, and the homeowner’s combined cost for services from both companies is 1,554
, which statements are true?
Select ALL that apply.
Answers
GPT-4o mini
To analyze the costs for both companies based on the information provided, we can set up the cost equations for Yard Oasis and Sand n’ Stone.
1. **Yard Oasis Cost**:
- **Fixed fee**: $168
- **Hourly rate**: $44
- **Total cost for \( x \) hours**:
\[
C_{\text{Yard Oasis}} = 168 + 44x
\]
2. **Sand n’ Stone Cost**:
- The hourly rate is 25% more than Yard Oasis's hourly rate:
- **Yard Oasis's hourly rate**: $44
- **Sand n’ Stone's hourly rate**:
\[
44 + 0.25 \times 44 = 44 + 11 = 55
\]
- **Total cost for \( x \) hours**:
\[
C_{\text{Sand n' Stone}} = 55x
\]
3. **Combined Cost**:
The combined total cost for both companies is given as $1,554:
\[
C_{\text{Yard Oasis}} + C_{\text{Sand n' Stone}} = 1554
\]
Substituting in the costs:
\[
(168 + 44x) + 55x = 1554
\]
Simplifying this:
\[
168 + 44x + 55x = 1554
\]
\[
168 + 99x = 1554
\]
\[
99x = 1554 - 168
\]
\[
99x = 1386
\]
\[
x = \frac{1386}{99}
\]
Calculating \( x \):
\[
x = 14
\]
So, the number of hours \( x \) the homeowner hired for landscaping services is 14.
Now, let’s compute the costs for both companies to be sure:
1. **Cost for Yard Oasis**:
\[
C_{\text{Yard Oasis}} = 168 + 44 \times 14 = 168 + 616 = 784
\]
2. **Cost for Sand n’ Stone**:
\[
C_{\text{Sand n' Stone}} = 55 \times 14 = 770
\]
3. **Combined Cost**:
\[
C_{\text{Yard Oasis}} + C_{\text{Sand n' Stone}} = 784 + 770 = 1554
\]
This checks out with the given total.
### True Statements:
Based on our analysis, we can conclude the following true statements:
- The total cost of landscaping services from Yard Oasis for 14 hours is $784.
- The total cost of landscaping services from Sand n’ Stone for 14 hours is $770.
- The combined total of $1554 confirms the calculations are correct.
- The hourly rate for Sand n’ Stone is $55.
Since I cannot see the specific statements you may have to choose from, the statements that can be concluded from the above work would be those relating to the calculated costs and hourly rates.
1. **Yard Oasis Cost**:
- **Fixed fee**: $168
- **Hourly rate**: $44
- **Total cost for \( x \) hours**:
\[
C_{\text{Yard Oasis}} = 168 + 44x
\]
2. **Sand n’ Stone Cost**:
- The hourly rate is 25% more than Yard Oasis's hourly rate:
- **Yard Oasis's hourly rate**: $44
- **Sand n’ Stone's hourly rate**:
\[
44 + 0.25 \times 44 = 44 + 11 = 55
\]
- **Total cost for \( x \) hours**:
\[
C_{\text{Sand n' Stone}} = 55x
\]
3. **Combined Cost**:
The combined total cost for both companies is given as $1,554:
\[
C_{\text{Yard Oasis}} + C_{\text{Sand n' Stone}} = 1554
\]
Substituting in the costs:
\[
(168 + 44x) + 55x = 1554
\]
Simplifying this:
\[
168 + 44x + 55x = 1554
\]
\[
168 + 99x = 1554
\]
\[
99x = 1554 - 168
\]
\[
99x = 1386
\]
\[
x = \frac{1386}{99}
\]
Calculating \( x \):
\[
x = 14
\]
So, the number of hours \( x \) the homeowner hired for landscaping services is 14.
Now, let’s compute the costs for both companies to be sure:
1. **Cost for Yard Oasis**:
\[
C_{\text{Yard Oasis}} = 168 + 44 \times 14 = 168 + 616 = 784
\]
2. **Cost for Sand n’ Stone**:
\[
C_{\text{Sand n' Stone}} = 55 \times 14 = 770
\]
3. **Combined Cost**:
\[
C_{\text{Yard Oasis}} + C_{\text{Sand n' Stone}} = 784 + 770 = 1554
\]
This checks out with the given total.
### True Statements:
Based on our analysis, we can conclude the following true statements:
- The total cost of landscaping services from Yard Oasis for 14 hours is $784.
- The total cost of landscaping services from Sand n’ Stone for 14 hours is $770.
- The combined total of $1554 confirms the calculations are correct.
- The hourly rate for Sand n’ Stone is $55.
Since I cannot see the specific statements you may have to choose from, the statements that can be concluded from the above work would be those relating to the calculated costs and hourly rates.