Question

Darren is going to the state fair. Each ride costs $6 to ride, and each exhibit costs $3 to view. Darren can spend at most $84 at the fair. 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)

Answer 1

Answer:

do zoo so zip so app el sup do so wish what sub ate

Step-by-step explanation:

ft takes see do stop

Answer 2

Answer:

(11, -2) is the solution set.

Step-by-step explanation:

Given that the ride costs $6 per ride, and each exhibit costs $3 per exhibit.

Darren can spend at most $84.

The inequality equation is given by

$6x + 3y \le84$

The graph is not given, so let us plot the inequality graph.

Setting x = 0, then

$y \le\dfrac{84}{3} \le28$

So, the coordinates can be written taken as (0, 28)

Similarly, take y = 0, then

$x \le\dfrac{84}{6} \le14$

So, the coordinates can be written taken as (14, 0).

Rewriting the given equation in standard slope - intercept form,

$6x + 3y \le84\implies y \le-2x+28$

So, the slope is m = -2, and the y - intercept is (0, 28).

Plot the with the y-intercept and slope or with the coordinates above.

Then the graph comes out to be as shown in the figure.

So, the left side region of the line satisfies the given inequality condition.

From the graph, which has a negative slope, it can be seen that with increase in x, y is decreasing.

So, from the given solution sets, A, B, and D have more y value than the x. Hence, these cannot be the solution sets.  

If we consider the option C, (11, -2) satisfies the condition $6x + 3y < 84$.

So, the correct answer is option C.    

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