Question

For a field trip, a bus company charges a flat fee plus an additional fee per student. for 25 students, the total cost is 132.50. if there are 30 students, the total cost is 145. which equation represents the total cost y of the field trip for x students?

Answer 1

The answer is y=5x+7.5

Answer 2

Answer:

$y=2.5x+70$

Step-by-step explanation:

First of all, this problem is modelled by a linear equation, where the ratio of change is the slope of the line.

Now, we know that $x$ represents students and $y$ represents the total cost.

The problem states that for 25 students, the total cost is $132.50. And for 30 students, the total cost is $145. This information represents two points

$(25,132.50)$ and $(30,145)$.

So, to find the equation, we first have to find the slope using these two point and the following formula

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{145-132.50}{30-25}=\frac{12.5}{5}=2.5$

This means the slope is 2.5

Now we use the point-slope formula to find the linear equation

$y-y_{1} =m(x-x_{1} )\\y-145=2.5(x-30)\\y=2.5x-75+145\\y=2.5x+70$

Therefore, the equation that models this problem is

$y=2.5x+70$

Where the flat fee is $70, and the fee per student is $2.5.