Question

1. a train travels from city a to city b and then back to city a. the table shows ticket purchase details for each leg of the trip. the cost per ticket is the same for each leg. explain whether there is enough information to determine the cost of one coach ticket.

destination	coach tickets	business class tickets	money collected
city b	170	100	$13,650

Explanation:

Step1: Define Variables

Let \( c \) be the cost of a coach ticket and \( b \) be the cost of a business - class ticket.
For the trip to City A, we have the equation: \( 150c + 80b=11550 \) (Equation 1)
For the trip to City B, we have the equation: \( 170c + 100b = 13650 \) (Equation 2)

Step2: Simplify Equations

First, simplify Equation 1 by dividing all terms by 5: \( 30c+16b = 2310 \) (Equation 1a)
Simplify Equation 2 by dividing all terms by 10: \( 17c + 10b=1365 \) (Equation 2a)

Step3: Eliminate a Variable

Let's multiply Equation 1a by 5: \( 150c+80b = 11550 \) (Equation 1b)
Multiply Equation 2a by 8: \( 136c+80b=10920 \) (Equation 2b)

Subtract Equation 2b from Equation 1b:
\((150c + 80b)-(136c + 80b)=11550 - 10920\)
\(150c+80b - 136c - 80b=630\)
\(14c=630\)

Step4: Solve for \( c \)

Divide both sides of the equation \( 14c = 630\) by 14:
\(c=\frac{630}{14}=45\)

Answer:

Yes, there is enough information. The cost of one coach ticket is \(\$45\).