SOLUTION: For their field studies in marine ecology, a group of students rented a boat for P360. However, seven students had to withdraw from the group and as a result, the share of each of
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Question 800786: For their field studies in marine ecology, a group of students rented a boat for P360. However, seven students had to withdraw from the group and as a result, the share of each of the remaining students was increased by P21.00. How many students were there in the original group?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
For their field studies in marine ecology, a group of students rented a boat for P360.
However, seven students had to withdraw from the group and as a result, the share of each of the remaining students was increased by P21.00.
How many students were there in the original group?
:
Let x = no. of students in original group
:
= original price per students
then
= actual price per student
:
Actual price - original price = 21
- = 21
multiply by x(x-7) to clear the denominators, resulting in:
360x - 360(x-7) = 21x(x-7)
360x - 360x + 2520 = 21x^2 - 147x
Combine as a quadratic equation
0 = 21x^2 - 147x - 2520
simplify, divide by 21
x^2 - 7x - 120 = 0
Factors to
(x-15) (x+8) = 0
the positive solution is all we want here
x = 15 students originally
:
:
See if that checks out, find the cost per student
360/8 = 45 (actual)
360/15= 24 (originally)
------------
diff: 21
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