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?

Question

Mathematics

Libby Simmons

2 June, 15:57

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?

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Answers (1)

Know the Answer?

Carmen Carpenter · Answer 1

242 Full Tickets were sold; and

3008 Student Tickets were sold.

Step-by-step 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.