Question

pA carnival sold tickets for $1.50 for adults and $1.00 for students. There were 54 tickets sold for a total of $70.50. Write a system of equations to represent the number of adult tickets, x, and the number of student tickets, y. Find the solution and explain what it means?​

Answer 1

• x + y = 54
• 1.50x +1.00y = 70.50
• x = 33; y = 21
• 33 adult tickets and 21 student tickets were sold

Explanation:

For such problems, it is convenient to write one equation for the total number of tickets sold

x + y = 54

and another equation for the total revenue collected from the sales

1.50x + 1.00y = 70.50

These equations are conveniently solved by eliminating the variable representing the lowest-price tickets (y). Here, we can simply subtract the first equation from the second:

(1.50x +1.00y) -(x + y) = (70.50) -(54)

0.50x = 16.50 . . . . simplify

x = 33 . . . . . . . . . . . multiply by 2

y = 54 -x = 21 . . . . . find the value of y

Given the definitions of the variables, (x, y) = (33, 21) means 33 adult ticket and 21 student tickets were sold.