Question

The drama club is selling T-shirts and caps to raise money for a spring trip. The caps sell for $5.00 each, and the T-shirts sell for $10.00 each. The drama club needs to raise at least $500.00 for the trip. The inequality that represents this situation is graphed, with x representing the number of caps sold and y representing the number of T-shirts sold. Which solution is valid within the context of the situation?

Answer 1

The correct answer to this question is C: (72,24).

Explanation:

We are given that:

The cost of 1 cap is $5 each

The cost of 1 t-shirt is $10 each

Let x be the number of caps sold

Let y be the number of t-shirt sold

In the context we are given that the drama club needs to raise at least $500 to go on the trip.

So based on this information we can create a inequality as:

the number of caps sold x (times) the cost of a single cap + the number of shirts x (times) the cost of a single t-shirt ≥ (greater than or equal to) 500

Inequality: 5x+10y ≥ 500 ( We used a greater than or equal to symbol because it said that the drama club need at least $500 for the trip.

Next we need to figure out how many caps and t-shirt were sold.

- We can already take out two of the options which are the two answer with negatives in them because we know that when you multiply a positive number with a negative number we get a negative number and we don't want that. (So Option A and Option D are out.)

Now all we do is plug x and y into our inequality equation ( 5x+10y ≥ 500 )

B) x=65 caps, y= 17.5 t-shirts ----> 5(65)+10(17.5) =500 which you get $500

YOU MAY THINK THIS IS THE ANSWER BUT! if you look closely at variable y it said they sold 17.5 t-shirt, but here there thing how do you sell 17 shirts and a half of shirt? Which means this option is also wrong!

C) x =72 caps, y =24 t-shirts ------> 5(72)+ 10(24)= $600 which is more than the original amount they were going for because it said at least $500.

So the correct option to this question is C, they sold 72 caps and 24 t-shirts and earned $600 dollars.

Answer 2

Answer: C

Step-by-step explanation: Each coordinate point is located within the solution set, as shown on the graph.

First, take out any solution that includes a negative number, since there cannot be a negative number of bags. So, (-2,10) and (9,-3) are not solutions.

Next, take out any solution that does not have all whole numbers because the bags are whole objects. So, (4.5,9) is not a solution.

So, (8,5) is a valid solution in the context of the situation.