ving Multi-Step Inequalities The student council wants to rent a ballroom for the junior prom. L is $1500 for 3 h and $125 for each additional half hour. Suppose $2125. What is the maximum number of hours for which they car 500 forin S00 xu 2000 2000 t25- 2125 h=4.5 hours
ving Multi-Step Inequalities The student council wants to rent a ballroom for the junior prom. L is $1500 for 3 h and $125 for each additional half hour. Suppose $2125. What is the maximum number of hours for which they car 500 forin S00 xu 2000 2000 t25- 2125 h=4.5 hours
Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Solving Multi-Step Inequalities**
The student council wants to rent a ballroom for the junior prom. The cost is $1500 for 3 hours and $125 for each additional half hour. Suppose they have $2125. What is the maximum number of hours for which they can rent the ballroom?
---
**Calculation Explanation**
Let \( h \) be the number of hours:
1. Calculate the base cost:
\[
500 \times 3 = 1500 \quad \text{(already for 3 hours)}
\]
2. Determine additional hours:
\[
500 \times 4 = 2000
\]
3. Add the increments for remaining budget:
\[
2000 + 125 = 2125
\]
4. Set and solve inequality:
\[
3 \leq h \leq 5
\]
5. Calculate maximum hours:
\[
h = 4.5 \text{ hours}
\]
Thus, the maximum number of hours they can rent the ballroom is 4.5 hours.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe927df63-f1e3-498b-a31a-923bb5077d27%2F1f7c774c-e00b-462e-996f-d121d317fbb0%2Fe98okqgm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solving Multi-Step Inequalities**
The student council wants to rent a ballroom for the junior prom. The cost is $1500 for 3 hours and $125 for each additional half hour. Suppose they have $2125. What is the maximum number of hours for which they can rent the ballroom?
---
**Calculation Explanation**
Let \( h \) be the number of hours:
1. Calculate the base cost:
\[
500 \times 3 = 1500 \quad \text{(already for 3 hours)}
\]
2. Determine additional hours:
\[
500 \times 4 = 2000
\]
3. Add the increments for remaining budget:
\[
2000 + 125 = 2125
\]
4. Set and solve inequality:
\[
3 \leq h \leq 5
\]
5. Calculate maximum hours:
\[
h = 4.5 \text{ hours}
\]
Thus, the maximum number of hours they can rent the ballroom is 4.5 hours.
![**Solving Multi-Step Inequalities**
The student council wants to rent a ballroom for the junior prom. The ballroom's rental rate is $1500 for 3 hours and $125 for each additional half hour. Suppose the student council raises $2125. What is the maximum number of hours for which they can rent the ballroom?
**Solution:**
Let \( h \) be the total number of hours the ballroom is rented.
1. Start with the base cost for 3 hours: $1500.
2. The additional cost is $125 for each additional half hour, equating to $250 for each additional hour.
3. We set up the inequality for the maximum cost allowed:
\[
1500 + 125 \times (2 \times (h - 3)) \leq 2125
\]
Simplifying gives:
\[
1500 + 250(h - 3) \leq 2125
\]
\[
1500 + 250h - 750 \leq 2125
\]
\[
250h + 750 \leq 2125
\]
\[
250h \leq 1375
\]
\[
h \leq 5.5
\]
4. Therefore, the maximum number of hours the council can rent the ballroom is **5.5 hours**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe927df63-f1e3-498b-a31a-923bb5077d27%2F1f7c774c-e00b-462e-996f-d121d317fbb0%2F90sfntc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solving Multi-Step Inequalities**
The student council wants to rent a ballroom for the junior prom. The ballroom's rental rate is $1500 for 3 hours and $125 for each additional half hour. Suppose the student council raises $2125. What is the maximum number of hours for which they can rent the ballroom?
**Solution:**
Let \( h \) be the total number of hours the ballroom is rented.
1. Start with the base cost for 3 hours: $1500.
2. The additional cost is $125 for each additional half hour, equating to $250 for each additional hour.
3. We set up the inequality for the maximum cost allowed:
\[
1500 + 125 \times (2 \times (h - 3)) \leq 2125
\]
Simplifying gives:
\[
1500 + 250(h - 3) \leq 2125
\]
\[
1500 + 250h - 750 \leq 2125
\]
\[
250h + 750 \leq 2125
\]
\[
250h \leq 1375
\]
\[
h \leq 5.5
\]
4. Therefore, the maximum number of hours the council can rent the ballroom is **5.5 hours**.
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