SOLUTION: The community theatre group puts on a play last month. 20 more adults attended than children adults tickets cost eight dollars each children's tickets cost three do

Question 1102935: The community theatre group puts on a play last month.
20 more adults attended than children
adults tickets cost eight dollars each
children's tickets cost three dollars each
the theatre group collected $1260. how many adult tickets were sold?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
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Let x = how many adults attended. Notice it is the same as how many adults tickets were sold. So the number of children attended was (x-20). 8*x + 3*(x-20) = 1260 is your value equation. ========================> 8x + 3x - 60 = 1260 ====> 11x = 1260 + 60 = 1320 ====> x = = 120. Answer. 120 adults.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

If you are studying algebra, then you should learn how to set up and solve the problem using formal mathematical methods, as demonstrated by the other tutor.

But it is also useful mental exercise to be able to solve a problem like this using less formal methods.

Here is how I would use logical reasoning to get a quick answer to the problem.

(1) The "extra" 20 adult tickets cost $20*8=$160; that means the remaining tickets cost a total of $1100.
(2) With the extra adult tickets accounted for, the remaining tickets are equal numbers of adult and children's tickets.
(3) The cost of 1 adult and 1 children's ticket is $8+$3 = $11.
(4) 1100/11 = 100; that means that, in addition to the 20 adult tickets already accounted for, 100 adult and 100 children's tickets were sold.
(5) So all together there were 100 children's tickets and 100+20=120 adult tickets sold.
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