Question

2) Natalie's school is selling tickets to a choral performance. On the first day of ticket sales the

school sold 7 senior citizen tickets and 6 child tickets for a total of $156. The school took in
$120 on the second day by selling 7 senior citizen tickets and 3 child tickets. Find the price of a
senior citizen ticket and the price of a child ticket.

Answer 1

both cost $12

Explanation:

Let's say the price of a senior citizen ticket is s dollars and the price of a child ticket is c dollars.

For, say, 7 senior citizen tickets, the cost would be s 7 times, or s * 7. Similarly, 6 child tickets would cost 6c. The total amount of (senior citizen ticket cost) + (child ticket cost) would equal the total sales.

Therefore,

first day:

7s + 6c = 156

second day:

7s + 3c = 120

7s + 6c = 156

7s + 3c = 120

we can solve this by solving for c in terms of s in one equation and plugging that into the other equation

7s + 6c = 156

subtract 7s from both sides to isolate the c and its coefficient

156 - 7s = 6c

divide both sides by 6 to isolate c

(156-7s)/6 = c

26-(7/6)s = c

plug that into the other equation

7s+3c = 120

7s + 3 (26-(7/6)s) = 120

7s + 78 - (21/6)s = 120

7s + 78 - (7/2)s = 120

(7/2)s + 78 = 120

subtract 78 from both sides to isolate s and its coefficient

(7/2)s = 42

multiply both sides by 2/7 to isolate s

12 = s

26 - (7/6)s = c

26 - 14 = c = 12