A total of 280 people attended the high school play. The admission prices were $

Question

A total of 280 people attended the high school play. The admission prices were $ 14 for adults, $ 6 for high school students, and $2 for children not yet in high school. The ticket sales totalled $ 1680.The principal suggested that next year they raise prices to $18 for adults, $7 for high school students, and $3 for children not yet in high school. He said that if exactly the same number of people attend next year, the ticket sales at the higher prices will total $ 2140. How many adults, high school students, and children not yet in high school attended this year?

Explanation / Answer

Let:
number of adults attending = A
number of high school students attending = H
number of children not yet in high school = C
We know that A + H + C = 280
Total ticket sales in first year : 14A + 6H + 2C = 1680

For next year, ticket sales :
18A + 7H + 3C = 2140
We are to find out A, H and C;

Subtracting 14A + 6H + 2C = 1680 from 18A + 7H + 3C = 2140 we get:
4A + H + C = 460
But H + C = 280-A
4a + 280 - A = 460
3A = 460-280 = 180

A = 180/3 = 60;
H+C = 280-60 = 220;
So H+C = 220;

Also, 14A + 6H + 2C = 1680
so 6H+2C = 1680-14*60 = 1680 - 840 = 840
6H + 2C = 840;
4H + 2(H+C) = 840
4H + 2*220 = 840
4H = 840 - 440 = 400
H = 400/4 = 100
So H = 100 and H+C = 220 so
C = 220-100 = 120;

Thus, A = 60; H = 100 and C = 120;

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