Here are the detailed solutions for each question from the uploaded image:

2018 #13

Problem:
Alejandra wants to spend part of $600 on a computer, leaving at least $250 in her account. The inequality $t + 250 \leq 600$ represents this situation. Solve for $t$, the amount she can spend.

Solution:

1. Start with the inequality:
   $t + 250 \leq 600$
2. Subtract 250 from both sides:
   $t \leq 600 - 250$ $t \leq 350$
3. This means Alejandra can spend up to $350 on the computer.

Correct Answer: C ($t \leq 350$)

2019 #31

Problem:
The area of a rectangle is 45.5 square inches, and the base is 7 inches. Find the height.

Solution:

1. The formula for the area of a rectangle is:
   $\text{Area} = \text{Base} \times \text{Height}$
2. Plug in the given values:
   $45.5 = 7 \times \text{Height}$
3. Solve for the height:
   $\text{Height} = \frac{45.5}{7}$ $\text{Height} = 6.5 \, \text{inches}$

Correct Answer: B (6.5 in.)

2021 #35

Problem:
The perimeter of a triangle is 104 units, and the combined length of two sides is 64 units. Find the length of the third side.

Solution:

1. The perimeter of a triangle is the sum of all three sides:
   $\text{Perimeter} = \text{Side}_1 + \text{Side}_2 + \text{Side}_3$ $104 = 64 + \text{Side}_3$
2. Solve for the third side:
   $\text{Side}_3 = 104 - 64$ $\text{Side}_3 = 40 \, \text{units}$

Correct Answer: C (40 units)

Let me know if you'd like further clarifications or details!

5 Questions for Expansion:

1. For the first problem, how would the inequality change if Alejandra only wanted $200 left in her account?
2. Could you calculate the area of a rectangle given the base and height instead?
3. How would the formula for the triangle problem change for a quadrilateral's perimeter?
4. What is the process for solving inequalities that involve fractions or decimals?
5. How can we generalize finding a missing side in polygons?

Tip:

When solving inequalities, always isolate the variable step by step and carefully reverse inequality signs when multiplying or dividing by a negative number!