3. Flyn is ordering t-shirts for all 8th graders at his school: T-shirts R-Us charges $6.25 per shirt with a one-time embroidery fee of $19. T-shirts Galore charges
$4 75 per shirt with a one-time embroidery fee of $43. Which inequality can be
used to find x, the minimum number of shirts that can be ordered so that the total
charge at T-shirts R-Us is less than the total charge at T-shirts Galore?
A. 6.25 + 19x < 4.75 + 43x
B. 6.25x + 19 < 4.75 + 43x
C. 6.25 + 19x < 4.75x + 43
D. 6.25x + 19 < 4.75x + 43

the answer is a

Step-by-step explanation:

Part A:

Look at the image attached to my answer for the graph of the inequalities.

There are two different lines provided, one with a more negative slope than the other. The shaded area between them represents the solution set.

The green line is 2x+y≤8, the blue line is x+y≥4

Part B:

To test if (8, 10) is included, substitute x = 8 and y = 10 into both inequalities. If it doesn't satisfy one of them, then it isn't included in the solution area.

2(8) + 10 ≤ 8

16 + 10 ≤ 8

26 ≤ 8... 26 is NOT less then or equal to 8

Thus, (8, 10) cannot be a solution since the inequality is not true.

Part C:

I'm going to choose a random point from the graph, (2, 3). For your answer, any point in the shaded region where both x and y is positive will work.

The point (2, 3) means that Sarah can buy 2 cupcakes and 3 pieces of fudge to get at least 4 pastries for her siblings while staying within her 8 dollar budget.

Let me know if you need any clarifications. Happy Studying~