Questions: Your school is planning a field trip to the zoo. There are two different bus companies that the school can use. Bus company A has a 35 rental fee plus 5 for each student. Bus company B has a 95 rental fee plus 3 for each student. How many students will need to go in order for the bus to cost the same from both companies?

Your school is planning a field trip to the zoo. There are two different bus companies that the school can use. Bus company A has a 35 rental fee plus 5 for each student. Bus company B has a 95 rental fee plus 3 for each student. How many students will need to go in order for the bus to cost the same from both companies?

Transcript text: 9. Your school is planning a field trip to the zoo. There are two different bus companies that the school can use. Bus company A has a $\$ 35$ rental fee plus $\$ 5$ for each student. Bus company B has a $\$ 95$ rental fee plus $\$ 3$ for each student. How many students will need to go in order for the bus to cost the same from both companies?

Solution

Solution Steps

To find the number of students needed for the cost to be the same from both companies, we need to set up an equation where the total cost from both companies is equal. Let $ x $ be the number of students. The cost for company A is $ 35 + 5x $ and for company B is $ 95 + 3x $. We set these two expressions equal to each other and solve for $ x $.

Step 1: Set Up the Cost Equations

Let $ x $ be the number of students. The total cost for bus company A is given by the equation: \[ C_A = 35 + 5x \] The total cost for bus company B is given by the equation: \[ C_B = 95 + 3x \]

Step 2: Set the Costs Equal

To find the number of students where the costs are the same, we set the two equations equal to each other: \[ 35 + 5x = 95 + 3x \]

Step 3: Solve for $ x $

Rearranging the equation gives: \[ 5x - 3x = 95 - 35 \] \[ 2x = 60 \] Dividing both sides by 2 results in: \[ x = 30 \]