Final answer:
To find the number of t-shirts and shirts that must be sold to make at least $600, we can write and solve the inequality 20x + 25y >= 600. By graphing the inequality or solving it algebraically, we can determine the range of values for x and y. Making a table of possible solutions can help visualize the different combinations of t-shirts and shirts that satisfy the inequality.
Step-by-step explanation:
To solve this problem, let's let x represent the number of t-shirts and y represent the number of shirts that must be sold. We need to write an inequality to represent the situation. Since t-shirts cost $20 each and shirts cost $25 each, the inequality will be 20x + 25y >= 600. To solve this inequality, you can graph it on a coordinate plane and shade the region above the line. You can also solve it algebraically by isolating either x or y and finding the range of values that satisfy the inequality.
Now let's make a table of at least five possible solutions. Let's start by assuming x = 0 and calculate y. If x = 0, then 25y >= 600, which simplifies to y >= 24. So the first solution is (0, 24). Now let's assume x = 1 and calculate y. If x = 1, then 20(1) + 25y >= 600, which simplifies to 25y >= 580. Solving for y, we get y>=23.2. Since y must be a whole number, the next possible solution is (1, 24).
Continue this process to find more solutions, and make sure to check if each solution satisfies the original inequality. The table should look something like this:
xy024 or greater124 or greater224 or greater324 or greater424 or greater