Find how many of each ticket was sold

Question

There were 200 tickets sold for a volleyball game. Tickets for students were $2 each and for adults were $3 each. The total amount collected was $530. How many of each type of ticket were sold?

Answer 1

A total of 586 people attended a banquet. A total of $9,423.70 in revenue was collected. Student tickets cost $12.95 and Adult tickets cost $17.95. Find the number of student and adult tickets sold.

Let: Student tickets = S

Let: Adult tickets = A

Given: Student ticket prices = $12.95

Given: Adult ticket prices = $17.95

Given: Total tickets sold = 586

Given: Total revenue = $9,423.70

S + A = 586                               (1)

12.95 S + 17.95 A = 9,423.70    (2)

Multiply equation (1) by –12.95

–12.95 S  – 12.95 A = –12.95 (586)

12.95 S + 17.95 A = 9,423.70

–12.95 S  – 12.95 A = –7,588.70

12.95 S + 17.95 A = 9,423.70

Add the two equations together. The S variables will drop out. That will leave us with A variables only. We then solve for A and substitute and solve for S.

5A = 1,835

Divide through by 5

A = 367 Adult tickets sold

Now substitute 367 for A and solve for S.

S + A = 586

S + 367 = 586

S = 219  Student tickets sold

Check 1

S + A = 586

219 + 367 = 586

586 = 586 Check

Check 2

12.95 S + 17.95 A = 9,423.70

12.95 (219) + 17.95 (367) = 9,423.70

2,836.05 + 6,587.65 = 9,423.70

9,423.70 = 9,423.70 Check

The final answer is, there were 219 Student tickets sold and 367 Adult tickets sold.

.

Answer 2

Let S = # tickets sold to students

Let A = # tickets sold to adults

 

Total tickets sold would be             A + S = 200

Total money made is                   2S + 3A = 530

 

Thus we have two simultaneous equations.  Let's take the two and solve using substitution.

 

Since A + S = 200 we can solve for A in terms of S ....   A = 200 - S

Substitute 200 - S in place of A in 2nd equation:  2S + 3(200-S) = 530

2S + 600 - 3S = 530

-S = 530 -600

-S = -70

S = 70

 

Thus we know there were 70 tickets sold to students.  Substituting back into A + S = 200 

gives us A + 70 = 200

A = 200 -70

A = 130

 

Thus 70 tickets were sold to students and 130 tickets were sold to adults