(1) File | C/Users/Admin/Deshtop/IAS\%2OFILES/FOURTH\%20QUARTER\%20LESSONS\%20SY24-25/Week\%20\%20(2)/Q4_LE_Mathem. 5. A cleaning service charges a fixed fee of PHP 1500 for a one-time cleaning d Problem session, plus PHP 200 per hour for additional cleaning time. If the cleaning session lasts for 4 hours, what will the total cost be? 7. A taxi company charges PHP 50 as a base fare for a ride, plus PHP 10 for every kilometer traveled. If the ride covers a distance of 8 kilometers, what will be the total fare? 8. A fitness trainer charges PHP 300 per session for personal training sessions, plus an additional PHP 50 for the use of equipment. What will be the total cost if a client schedules 3 sessions and uses equipment for 2 of them? 9. A movie theater charges PHP 200 for a movie ticket and an additional PHP 50 for a large popcorn. What will be the total cost if a person buys 2 tickets and 1 large popcorn? 10. A music streaming service charges a monthly subscription fee of PHP 150 and an additional PHP 50 for a family plan upgrade. If someone subscribes to the

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Let's solve each of the problems step by step.

### Problem 5: Cleaning Service Cost
1. **Fixed Fee**: PHP 1500
2. **Hourly Rate**: PHP 200
3. **Duration**: 4 hours

**Total Cost Calculation**:
$$
\text{Total Cost} = \text{Fixed Fee} + (\text{Hourly Rate} \times \text{Duration})
$$
$$
\text{Total Cost} = 1500 + (200 \times 4)
$$
Calculating the hourly cost:
$$
200 \times 4 = 800
$$
Now, adding the fixed fee:
$$
\text{Total Cost} = 1500 + 800 = 2300
$$

**Total Cost for Cleaning Service**: PHP 2300

---

### Problem 7: Taxi Fare Calculation
1. **Base Fare**: PHP 50
2. **Cost per Kilometer**: PHP 10
3. **Distance**: 8 kilometers

**Total Fare Calculation**:
$$
\text{Total Fare} = \text{Base Fare} + (\text{Cost per Kilometer} \times \text{Distance})
$$
$$
\text{Total Fare} = 50 + (10 \times 8)
$$
Calculating the distance cost:
$$
10 \times 8 = 80
$$
Now, adding the base fare:
$$
\text{Total Fare} = 50 + 80 = 130
$$

**Total Fare for Taxi Ride**: PHP 130

---

### Problem 8: Fitness Trainer Cost
1. **Cost per Session**: PHP 300
2. **Equipment Fee**: PHP 50
3. **Number of Sessions**: 3
4. **Sessions with Equipment**: 2

**Total Cost Calculation**:
- Cost for sessions without equipment: 
$$
\text{Cost without Equipment} = \text{Cost per Session} \times (\text{Number of Sessions} - \text{Sessions with Equipment}) = 300 \times (3 - 2) = 300
$$
- Cost for sessions with equipment:
$$
\text{Cost with Equipment} = (\text{Cost per Session} + \text{Equipment Fee}) \times \text{Sessions with Equipment} = (300 + 50) \times 2 = 350 \times 2 = 700
$$
- Total Cost:
$$
\text{Total Cost} = \text{Cost without Equipment} + \text{Cost with Equipment} = 300 + 700 = 1000
$$

**Total Cost for Fitness Training**: PHP 1000

---

### Problem 9: Movie Theater Cost
1. **Cost per Ticket**: PHP 200
2. **Cost for Large Popcorn**: PHP 50
3. **Number of Tickets**: 2
4. **Number of Popcorns**: 1

**Total Cost Calculation**:
$$
\text{Total Cost} = (\text{Cost per Ticket} \times \text{Number of Tickets}) + (\text{Cost for Large Popcorn} \times \text{Number of Popcorns})
$$
$$
\text{Total Cost} = (200 \times 2) + (50 \times 1)
$$
Calculating the ticket cost:
$$
200 \times 2 = 400
$$
Calculating the popcorn cost:
$$
50 \times 1 = 50
$$
Now, adding both costs:
$$
\text{Total Cost} = 400 + 50 = 450
$$

**Total Cost for Movie Theater**: PHP 450

---

### Problem 10: Music Streaming Service Cost
1. **Monthly Subscription Fee**: PHP 150
2. **Family Plan Upgrade**: PHP 50

**Total Cost Calculation**:
$$
\text{Total Cost} = \text{Monthly Subscription Fee} + \text{Family Plan Upgrade}
$$
$$
\text{Total Cost} = 150 + 50 = 200
$$

**Total Cost for Music Streaming Service**: PHP 200

---

### Summary of Total Costs:
- Cleaning Service: PHP 2300
- Taxi Fare: PHP 130
- Fitness Training: PHP 1000
- Movie Theater: PHP 450
- Music Streaming Service: PHP 200
- Cleaning Service: PHP 2,300 - Taxi Fare: PHP 130 - Fitness Training: PHP 1,000 - Movie Theater: PHP 450 - Music Streaming Service: PHP 200

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