A theater sold 150 tickets for a play, some at 12 for adults and the rest at 7 for children. Total ticket sales were $1,400. How many…

Let $a$ be the number of adult tickets and $c$ the number of child tickets. Then $a + c = 150$ and $12a + 7c = 1400$. Substitute $c = 150 - a$: $12a + 7(150 - a) = 1400$, so $12a + 1050 - 7a = 1400$. Then $5a = 350$ and $a = 70$, choice A. Check: 70 adults give $840, 80 children give $560, and the total is $1,400. Choice B (80) is the number of child tickets, a common mix-up when reading what the question asks. Choice C (100) and choice D (50) are guesses that fail the revenue check, since they give totals of $1,550 and $1,300 respectively.