Question

The theater club sells a total of 101 tickets to its first play. A student ticket costs $1. An adult ticket costs $2.50. Total ticket sales are $164. Part A Let x represent the number of adult tickets and y represent the number of student tickets. Write a system of equations in terms of x and y to model the situation.

Answer 1

Answer: A) x+ y = 101--------Equation 1

2.50x + y= 164----- Equation 2

B) X= 49 adult tickets

y= 52 student tickets

Explanation:

Step 1

Let x represent the number of adult tickets

and y represent the number of student tickets

Such that the total n umber of tickets sold can be expressed as

x+ y = 101

Also given that student ticket costs $1 and An adult ticket costs $2.50 such that the equation to represent The total sales will be

2.50x + 1y= $164

Step 2

The system of equations in terms of x and y to model the situation are given as

x+ y = 101--------Equation 1

2.50x + y= 164----- Equation 2

Solvng

x+y =101-----1

making y the subject formulae

y=101-x

Substituting y= 101-x into equation 2 and solvng out

2.50 + 101-x =164

1.50 x= 164-101

1.50x=63

x=63/1.50

x=42

Putting the value of x= 42 into equation 1 to find y

x+y=101

y= 101-42

y=59