For a field trip, a bus company charges a flat fee plus an additional fee per student. For 25 students, the total cost is $167.50. If there are 70 students, the total cost is $370.00. Write an equation that represents the total cost y of the field trip for x students. What would the total cost be if 110 students went on the field trip?
cost=flat+numberkids*costperkid
370=flat+70*costperkid
167.5=flat+25*costperkid
subtract second equation from first..
370-167.5=45*costperkid
solve for costper kid, then go back and solve for flat.
Something tells me this is not the real bobpursley ...
Thanks, Steve.
Will be deleted and banned within a couple of minutes.
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 $145.00. Write an equation that represents the total cost y of the field trip for x students. What would the total cost be if 85 students went on the field trip?
To write an equation that represents the total cost ($y) of the field trip for a given number of students ($x), we need to consider the two given scenarios:
1. For 25 students, the total cost is $167.50.
2. For 70 students, the total cost is $370.00.
Let's break down the steps to find the equation:
Step 1: Determine the flat fee
To find the flat fee, we need to subtract the additional fee per student from the total cost when there are no students. When the number of students is 0, the total cost ($y) must be equal to the flat fee. Therefore, the flat fee is the y-intercept of the equation.
Using equation (1):
167.50 = flat fee + additional fee per student * 25
From equation (1), we can isolate the flat fee:
flat fee = 167.50 - additional fee per student * 25
Step 2: Determine the additional fee per student
We can find the additional fee per student by subtracting the flat fee from the total cost when there are enough students to cover only the additional fee per student. The difference between the total cost and the flat fee will give us the cost attributable to the additional fee per student.
Using equation (2):
370.00 = flat fee + additional fee per student * 70
From equation (2), we can isolate the additional fee per student:
additional fee per student = (370.00 - flat fee) / 70
Step 3: Write the equation
Now that we know the flat fee and the additional fee per student, we can write the equation for the total cost of the field trip.
y = flat fee + additional fee per student * x
Substituting the values found in step 1 and step 2:
y = (167.50 - additional fee per student * 25) + additional fee per student * x
Step 4: Simplify the equation
We can simplify the equation further by distributing the additional fee per student across the terms:
y = 167.50 - 25 * additional fee per student + additional fee per student * x
Finally, we can simplify it even more:
y = 167.50 + additional fee per student * (x - 25)
Now, to determine the total cost if 110 students go on the field trip, we substitute x = 110 into the equation:
total cost for 110 students (y) = 167.50 + additional fee per student * (110 - 25)
To find the value of additional fee per student, we use the values we calculated earlier.
Then, we can calculate the total cost for 110 students.