Question

select the correct answer. at a zoo, youth tickets cost $5 and adult tickets cost $9. a group that purchased x youth tickets and y adult tickets spent $90 on tickets. what is the domain of the relationship? a. ( x leq 5 ) b. ( 0 leq x leq 5 ) c. ( 0 leq x leq 18 ) d. ( x leq 18 )

Explanation:

Step1: Set up cost equation

$5x + 9y = 90$

Step2: Solve for y in terms of x

$y = \frac{90 - 5x}{9}$

Step3: Define valid ticket counts

$x \geq 0$, $y \geq 0$, and $x,y$ are integers.

Step4: Find x range from y ≥ 0

$\frac{90 - 5x}{9} \geq 0 \implies 90 - 5x \geq 0 \implies x \leq 18$

Step5: Combine constraints for domain

$0 \leq x \leq 18$ (x must be non-negative integer values that make y non-negative integer, but the overall domain interval is this range)

Answer:

C. $0 \leq x \leq 18$