Question

1. to raise money for after school programs at the elementary school, a group of parents are holding a weekend of games in the community center. they charge $8 per person for entry into the event. the group would like to earn at least $600, after paying for the cost of renting the community center, which is $40 an hour.

a. if x represents the number of entry tickets sold and y represents the hours of rental, which inequality represents the constraints in the situation?
a ( 8x - 40y < 600 )
b ( 8x - 40y leq 600 )
c ( 8x - 40y > 600 )
d ( 8x - 40y geq 600 )
b. the line is the graph ( 8x - 40y = 600 ). select all the points whose ( (x,y) ) values represent the group reaching its fundraising goal. explain or show your reasoning (words or mathematically).
yes or no
a.

b.

c.

Explanation:

Step1: Define income and cost

Income from tickets: $8x$, Rental cost: $40y$

Step2: Set up inequality for goal

Net earnings ≥ $600$, so $8x - 40y \geq 600$

Step3: Test point A(100,10)

Substitute into $8x - 40y$: $8(100) - 40(10) = 800 - 400 = 400$

Step4: Test point B(180,21)

Substitute into $8x - 40y$: $8(180) - 40(21) = 1440 - 840 = 600$

Step5: Test point C(200,5)

Substitute into $8x - 40y$: $8(200) - 40(5) = 1600 - 200 = 1400$

Answer:

a. D. $8x - 40y \geq 600$
b.

• A. No, since $400 < 600$, net earnings are below the goal.
• B. Yes, since $600 = 600$, net earnings meet the goal.
• C. Yes, since $1400 > 600$, net earnings exceed the goal.