Answer:

Let's use the variable 'k' to represent the number of turns on the kongs and 'c' to represent the number of turns on the cans.

The number of tokens needed for each turn on the kongs is 3, and the number of tokens needed for each turn on the cans is 5.

The total number of tokens he can buy is limited to 26.

We can write the inequality as follows:

3k + 5c ≤ 26

Now, let's shade the region on the number plane to represent the feasible region:

Start by graphing the line corresponding to the equation 3k + 5c = 26. This line represents the boundary of the feasible region.

To graph the line, first find two points on the line. For example, when k = 0, c = 26/5 ≈ 5.2, and when c = 0, k = 26/3 ≈ 8.67. Plot these two points and draw the line passing through them.

Since the inequality is "less than or equal to," we need to shade the region below the line.

Now, why are there limits to where you can shade?

The limits to where you can shade are determined by the constraints of the problem. In this case, the constraint is that Ken's can only buy 26 tokens. Therefore, any combination of 'k' and 'c' that results in a total of more than 26 tokens is not feasible and should not be shaded.

By graphing the feasible region, we can visually see the combinations of 'k' and 'c' that satisfy the constraint. All the points below the line represent valid combinations where the total number of tokens used for turns on both the kongs and the cans is 26 or less, which is within Ken's budget. Points above the line are not valid in this context because they would require more tokens than ken can afford.