AlgebraMediumSystem from a word problem
Algebra practice question
A theatre sold 40 tickets for a total of $275. Adult tickets cost $8 each and child tickets cost $5 each. How many adult tickets were sold?
Answer: 25
Let a be adult tickets and c child tickets: a + c = 40 and 8a + 5c = 275. Substitute c = 40 − a: 8a + 5(40 − a) = 275, so 8a + 200 − 5a = 275, 3a = 75, a = 25. Check: 25 adult + 15 child = 40 tickets; 200 + 75 = 275 dollars.
Common wrong answers
- If you answered 15
- 15 is the number of CHILD tickets. The question asks for adult tickets: 40 − 15 = 25.
- If you answered 35
- 35 would come from (275 − 5·8)/... a misreading of which price goes with which count. Set up a + c = 40 and 8a + 5c = 275 and solve.
- If you answered 40
- 40 is the total number of tickets of both kinds, not the adult tickets alone.
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