Equation question on description

Question

a group of students are going on a picnic. The total expenditure will be equally shared among students. if each student pays $65, the amount collected will be $300 less than the total expenditure. if each student pays $75, the amount collected will be $100 more than the total expenditure. find the number of students joining the picnic.

Answer 1

x = number of students

y = total expenditure

 

65x = y - 300

75x = y + 100

 

Solve for x and y.  Subtract top equation from bottom equation.

 

10x = 400

 

x = 40

 

y + 100 = 75x ⇒

 

y = 75x - 100 = 75(40) - 100 = 2900

 

There are 40 students and the total expenditure is $2900.

 

Test these answers.