Martha has a $75 gift certificate to spend at an online comic book store. Including tax, the premium comics cost $8 each and the regular comics cost $5 each. Martha wants to buy at least 3 premium comics.
Graph a system of inequalities that represents this story. One inequality should represent Martha's budget constraint, and the other inequality should represent the number of premium comics she buys.
Select a line to change it between solid and dotted. Select a region to shade it.
Let's use the variable $x$ to represent the number of premium comics Martha buys, and variable $y$ to represent the number of regular comics she buys.
Martha's budget constraint can be represented by the inequality:
$$8x + 5y \leq 75$$
Since Martha wants to buy at least 3 premium comics, the inequality representing the number of premium comics she buys is:
$$x \geq 3$$
Now, let's graph these inequalities.
Graph for the budget constraint:
- Line: $8x + 5y = 75$
- Type: Solid line to represent Martha can spend the full $75 gift certificate
- Shading: Below the line to represent the budget constraint
Graph for the number of premium comics:
- Line: $x = 3$
- Type: Solid line to represent Martha buys at least 3 premium comics
- Shading: To the right of the line to represent the number of premium comics she buys
Please note that the lines may not intersect on this graph as Martha may not be able to spend the full $75 on comic books while buying at least 3 premium comics.