7. Airline fares for a flight from Dallas to Austin are $$ \$ 30 $$ for first class and $$ \$ 25 $$ for tourist class. If a flight had 52 passengers who paid $$ \$ 1360 $$, how many first class and tourist class passengers were there?

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UpStudy AI · Accepted Answer

To determine the number of first class and tourist class passengers on the flight from Dallas to Austin, we can set up a system of equations based on the given information.

**Let:**
- $$ f $$ = number of first class passengers
- $$ t $$ = number of tourist class passengers

**Given:**
1. The total number of passengers is 52:
   $$
   f + t = 52 \quad \text{(Equation 1)}
   $$
2. The total revenue from fares is \$1360:
   $$
   30f + 25t = 1360 \quad \text{(Equation 2)}
   $$

**Steps to Solve:**

1. **Solve Equation 1 for $$ f $$:**
   $$
   f = 52 - t
   $$
   
2. **Substitute $$ f = 52 - t $$ into Equation 2:**
   $$
   30(52 - t) + 25t = 1360
   $$
   
3. **Expand and simplify:**
   $$
   1560 - 30t + 25t = 1360
   $$
   $$
   1560 - 5t = 1360
   $$
   
4. **Solve for $$ t $$:**
   $$
   -5t = 1360 - 1560
   $$
   $$
   -5t = -200
   $$
   $$
   t = \frac{-200}{-5} = 40
   $$
   
5. **Find $$ f $$ using the value of $$ t $$:**
   $$
   f = 52 - 40 = 12
   $$

**Conclusion:**
- **First Class Passengers:** 12
- **Tourist Class Passengers:** 40

**Verification:**
- Total passengers: $$ 12 + 40 = 52 $$ ✓
- Total revenue: $$ (12 \times 30) + (40 \times 25) = 360 + 1000 = 1360 $$ ✓

**Answer:**  
There were 12 first class passengers and 40 tourist class passengers on the flight.
There were 12 first class passengers and 40 tourist class passengers on the flight.

7. Airline fares for a flight from Dallas to Austin are \( \$ 30 \) for first class and \( \$ 25 \) for tourist class. If a flight had 52 passengers who paid \( \$ 1360 \), how many first class and tourist class passengers were there?

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