Formulate inequalities for the following scenarios: 1. A plane has a capacity of 200 passengers. 2. A company has a budget of sh 40,000 per day for workers, with skilled workers costing sh 1,600 and u

Let $x$ be the number of first-class passengers.
Let $y$ be the number of second-class passengers.

The total number of passengers ($x + y$) should not exceed 200, meaning it must be less than or equal to 200.

The inequality is: $\boxed{x + y \le 200}$

2.

Let $x$ be the number of skilled workers.
Let $y$ be the number of unskilled workers.
Skilled workers are paid sh 1 600 per day.
Unskilled workers are paid sh 800 per day.

Total cost = $1600x + 800y$.

The total amount for hiring workers should not exceed sh 40 000.

The inequality in its simplest form is: $\boxed{2x + y \le 50}$

3.

Let $x$ be the number of invited guests.
Cost for snacks per guest = sh 200.
Cost for cake ingredients = sh 1 000.

Total expenditure = $200x + 1000$.

Linet's budget is sh 5 000, so the total expenditure should not exceed this amount.

The inequality is: $\boxed{200x + 1000 \le 5000}$

4.

Let $x$ be the number of elite athletes.
Let $y$ be the number of average athletes.
Registration fee for elite athletes = sh 5 000.
Registration fee for average athletes = sh 1 000.

Total amount raised = $5000x + 1000y$.

The planning committee intends to raise at least sh 1 000 000, meaning the amount raised must be greater than or equal to sh 1 000 000.

The simplified expression (inequality) is: $\boxed{5x + y \ge 1000}$

5.

Let $X$ be the number of type X buses.
Let $Y$ be the number of type Y buses.
Capacity of type X bus = 64 learners.
Capacity of type Y bus = 48 learners.

Total capacity = $64X + 48Y$.

The school needs to take 384 learners, so the total capacity must be at least 384.

The linear inequality is: $\boxed{4X + 3Y \ge 24}$