Question

Full-price tickets for a concert cost $ 58.50. Students can purchase a discounted ticket for $ 48.50. If a total of 3250 tickets are sold and if the total amount of ticket sales was $ 160,045​a) how many​ full-price tickets were​ sold? ​b) how many student tickets were​ sold?

Answer 1

242 Full Tickets were sold; and

3008 Student Tickets were sold.

Explanation:

Let the number of full tickets sold=x

Let the number of student tickets sold =y

A total of 3250 tickets were sold, therefore:

• x+y=3250

Cost of a Full Ticket =$58.50.

Cost of a Discounted Ticket=$48.50

Total Amount =(58.50. X Number of Full Tickets sold)+(58.50 X Number of Student Tickets sold)

Total amount of ticket sales was $ 160,045

Therefore:

• 58.50x+48.50y=160045

We solve the two equations simultaneously to obtain the values of x and y.

From the First Equation, x=3250-y

Substitute x=3250-y into the Second Equation.

58.50x+48.50y=160045

58.50(3250-y)+48.50y=160045

Open the brackets

190125-58.50y+48.50y=160045

-10y=160045-190125

-10y=-30080

Divide both sides by -10

y=3008

Recall: x=3250-y

x=3250-3008

x=242

Therefore:

242 Full Tickets were sold; and

3008 Student Tickets were sold.