A local theater sells out for their show. They sell at 500 tickets for a total purse of $8,010.00.
The tickets were priced at $15.00 for students, $12.00 for children, and $18.00 for adults. If the band sold three times as many adult tickets as children's tickets, how many of each type were sold?
The bot somehow assumed that the number of student and children tickets
were the same, even though it was not stated. Besides that it never used
the fact that 500 tickets were sold. So the bot's answer is bogus!!
number of children tickets --- x
number of student tickets --- y
number of adult tickets ---- 3x
x + y + 3x = 500
y = 500 - 4x
12x + 15(500-4x) + 18(3x) = 8010
12x + 7500 - 60x + 54x = 8010
6x = 510
x = 85
so they sold 85 children tickets
255 adult tickets and
160 student tickets.
check: 85(12) + 160(15) + 255(18) = 8010
and 85+160+255 = 500
My answer is correct, the bot is wrong!!
Let's assume the number of children's tickets sold is x.
According to the problem, the number of adult tickets sold would be three times that of children tickets. So the number of adult tickets sold would be 3x.
Now, we can use this information to create an equation:
15x + 12x + 18(3x) = 8010
Simplifying this equation, we get:
15x + 12x + 54x = 8010
81x = 8010
x = 98.7
Since we can't have a fractional number of tickets, we'll have to round up the number of children's tickets sold to 99.
Thus, the number of children's tickets sold was 99, the number of adult tickets sold was 3x or 297, and the number of student tickets sold would be:
500 - (99 + 297) = 104
Therefore, 99 children's tickets, 297 adult tickets, and 104 student tickets were sold.