question is in the description because it was too long

Question

The Little Town Arts Center charges $25 for adults, $14 for seniors, and $7 for children for their Sunday afternoon performances. This past Sunday, the paid revenue was $11680 for 790 tickets sold. There were 40 more children than adults. How many tickets of each type were sold?

Answer 1

A+C+S = 790

C = A+40

25A + 7C + 14S = 11680

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substitutes the second equation into the first and third equations

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A + A+40 + S = 790

25A + 7(A+40) + 14S = 11680

2A + S = 750

S = 750 - 2A

32A + 14S + 280 = 11680

32A + 14S = 11400

32A + 14(750 - 2a) = 11400

32A + 10500 - 28A = 11400

4A = 900

A = 225

C = A+40 = 265

S = 300