2012-05-07 09:00:44

For the school carnival, the administration offered two types of tickets: students could purchase tickets for $5 each, while non-students could purchase tickets for $8 each. The school ended up selling 140 tickets in total and raising $850 from ticket sales. What is the difference between the number of student and non-student tickets sold?

(A) 30 tickets
(B) 40 tickets
(C) 50 tickets
(D) 70 tickets
(E) 90 tickets

The correct answer is B

Explanation: To solve word problems such as this one, set up two equations to keep track of all the information. Let S be the number of student tickets sold and N be the number of non-student tickets sold. The total number of tickets sold, 140, is the sum of S and N, while the total amount of money raised is based on the sum of the amount of money raised by S and the amount of money raised by N. Therefore, the two equations you need are:

S + N = 140 &    5S + 8N = 850

Solve the first equation for N (or S, it really doesn't matter) by subtracting S from both sides to get N = 140 - S. Now, substitute 140 - S in for N in the second equation:

5S + 8(140 - S) = 850, which simplifies to 5S + 1120 - 8S = 850 or 1120 - 3S = 850.

Subtract 850 from both sides and add 3s to both sides to get 270 = 3S, meaning S = 90. Thus, 90 student tickets were sold. Plug 90 back in for S in the first equation to get

90 + N = 140

By subtracting 90 from both sides, you will get N = 50.

Finally, to find the difference between the number of student and non-student tickets sold, simply subtract S - N, or 90 - 50, to get 40, making choice B correct.