A small theatre has a student rate of 3 per ticket and a regular rate of 10 per ticket. Last night 243 of collected from the sale of tickets. There were more than 50 but less than 60 tickets sold. How many student tickets were sold?
2026-02-23 01:08:07.1771808887
A small theatre has a student rate of 3 per ticket and a regular rate of 10 per ticket
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Let $a$ be the number of student tickets sold and $b$ number of general tickets sold. You can calculate a range for $a$ using the range of tickets sold. We know $3a + 10b = 243$. Then, we have $$ 50 < a+b < 60 $$ $$ 50 < a + (243-3a)/10 < 60 $$ $$ 36.7 < a < 51 $$ So, we know the value for $a$ must produce a last digit of 3, so $a=41$. Any other choice for $a$ would not produce the 3 in that range. Then, $b=12$, and $ a+b=53$ and $50<53<60$. Therefore, 41 student tickets were sold.