The cost of a class picnic was $42. If 14 more students had come, the cost per student would have been 20 cents less. How much was the cost per student?

Let X be the number of students.

cost per pen of X students =42/X.

If 14 morte studenst added

cost per pen = 42/(x+14).

Now 42/x-42(x+14)=1/5.

Multiply thru by 5x(x+14) to get.

42*5*(x+14)-42x*5=x*(x+14).

210x+2940-210x=x^2+14x.

x^2+14x-2940=0.

x = [-14 +- sqrt(14^2 - 4*1*-2940)]/2

Take only posituve value

x = 47.67

The cost of original pen  x=$47.67.