Final answer:
To find the minimum number of each type of ticket that the cashier had to sell for the total receipts to be at least $1000, you can set up an equation and solve for the number of children's tickets. The minimum number of children's tickets is 57, and the minimum number of adult tickets is 107.
Step-by-step explanation:
To find the minimum number of each type of ticket that the cashier had to sell for the total receipts to be at least $1000, we can set up an equation. Let's say the number of children's tickets sold is 'x'. Then, the number of adult tickets sold would be 'x + 50'. We can multiply the number of children's tickets by $5.50 and the number of adult tickets by $6.50 and set the sum equal to or greater than $1000:
5.50x + 6.50(x + 50) ≥ 1000
Simplifying the equation, we get:
5.50x + 6.50x + 325 ≥ 1000
Combining like terms, we have:
12x + 325 ≥ 1000
Subtracting 325 from both sides of the inequality:
12x ≥ 675
Dividing both sides by 12, we find:
x ≥ 56.25
Since the number of children's tickets must be a whole number, the minimum number of children's tickets the cashier had to sell is 57. Therefore, the minimum number of adult tickets is 57 + 50 = 107.