In addition to the standard airfare, a particular airline charges passengers for two kinds of travel service: $25 to check a bag and $15 to upgrade to priority boarding. If the airline collected $3,065 in baggege and priority boarding fees from 145 travel services on two flights combined, which of the following system of equations could be used to determine the number of bags checked (b) and the number of priority boarding upgrades (p) purchased on the two flights?

Options

A. `b+p=145times2`
`25b+15p=3,065times2`
B. `b+p=145`
`25b+15p=3,065`
C. `b+p=145`
`15b+25p=3,065`
D. `b+p=(145)/(2)`
`15b+25p=(3,065)/(2)`

Explanation

To solve the problem, we need to set up a system of equations based on the information provided.

### Step 1: Define the Variables
Let:
- \( b \) = number of bags checked
- \( p \) = number of priority boarding upgrades purchased

### Step 2: Set Up the First Equation
According to the problem, the airline collected a total of $3,065 from baggage and priority boarding fees. The fee for checking a bag is $25, and the fee for upgrading to priority boarding is $15. Therefore, the total amount collected can be expressed as:
\[ 25b + 15p = 3065 \]

### Step 3: Set Up the Second Equation
The problem also states that there were a total of 145 travel services (which includes both bags checked and priority boarding upgrades). This can be expressed as:
\[ b + p = 145 \]

### Step 4: Write the System of Equations
Now we can write the system of equations based on the two equations we have set up:
1. \( 25b + 15p = 3065 \)
2. \( b + p = 145 \)

### Final System of Equations
Thus, the system of equations that can be used to determine the number of bags checked (\( b \)) and the number of priority boarding upgrades (\( p \)) is:
\[ \begin{align*} 25b + 15p &= 3065 \\ b + p &= 145 \end{align*} \]