How to put a word problem into inequality form

Question

 
Word Problem: Tickets for the school play cost $3 for students and $6 for adults. The drama club hopes to bring in at least $450 in sales, and the auditorium has 120 seats. Let a represent the number of adult tickets, and let s represent the number of student tickets. a.) Write a system of inequalities representing this situation. b.) Show the solutions to the system of inequalities by graphing.  

Answer 1

a.) Write a system of inequalities representing this situation

 

Let No. of adult = a

no.of student = s

 

the auditorium has 120 seats.

a+s≤ 120

 

at least means greater than or equal to

 

6a+3s ≥ 450

b.) Show the solutions to the system of inequalities by graphing.

you have to graph above 2 inequality and shade the common part which is solution

 

 

Answer 2

A+s <=120

 

6A + 3S>=450 --->  2A + s >= 150 ----> s >= 150- 2A

 

A + (150 -2A) <= 120

 

150 - A <= 120

 

-A <= -30

 

A >= 30

 

s >= 150 - 2(30) = 150 - 60 = 90 

 

30 adult tickets

90 student tickets

 

check: 6(30) + 3(90) = 180 + 270  = 450