Question

the inequality and graph that represent this situation are shown, with x representing the number of rides darren can ride and y representing the number of exhibits he can view.
6x + 3y ≤ 84
which solution is valid within the context of the situation?
a. (9,10)
b. (8.5,11)
c. (11,-2)
d. (-3,15)

Explanation:

Step1: Check context validity

x (rides) and y (exhibits) must be non - negative integers (can't have negative or fractional number of rides/exhibits). So eliminate options with negative or non - integer x/y. Option B has x = 8.5 (fractional rides), Option C has y=-2 (negative exhibits), Option D has x = - 3 (negative rides).

Step2: Check inequality for A

Substitute x = 9, y = 10 into \(6x + 3y\): \(6\times9+3\times10=54 + 30=84\). Since \(84\leq84\) is true, and x,y are non - negative integers.

Answer:

A. (9,10)