Question

a college charters a bus for 1700 dollars to take a group to a museum. when six more students joined the trip the cost per student drops by $7.50. How many students were in the original group?

Answer 1

Answer: The answer is 34 students.

Step-by-step explanation: Given that a college charters a bus for 1700 dollars to take a group to a museum. Also, when six more students joined the trip the cost per student is $7.50 less. We need to find the number of students in the original group.

Let 'n' be the number of students in the original group and 'p' be the cost per student originally. So, we have

`n* p=1700,\\(n+6)(p-7.5)=1700.`

Comparing both the equations, we can write

`np=(n+6)(p-7.5)\\\\Rightarrow np=np+6p-7.5n-45\\\\\Rightarrow 6p-7.5n=45\\\\\Rightarrow 60p-75n=450\\\\\Rightarrow 4p-5n=30.`

Substituting the value of 'p' from the first equation, we have

`4* (1700)/(n)-5n=30\\\\\\\Rightarrow n^2+6n-1360=0\\\\ \Rightarrow (n+40)(n-34)=0\\\\\Rightarrow n=-40,~~34.`

Since the number of students cannot be negative, so n = 34.

Thus, 34 students were there in the original group.