5 questions

I need the following solved and show work. 

1. The Highway Patrol can spend a maximum of $240,000 on new vehicles this year.  The can purchase a fully equipped compact care for $30,000 or a fully equipped full-size care for $40,000.  Graph the region that shows the number of cars of each type that could be purchased within the budget.

Show your graph.

Define both axis.

Explain your reasoning and solution.

2. Solve for the two variables.  Explain your solution and the solution method you used.  Show your work and your mathematics.

-3q+r=3

2q-3r=5

3. Pick one of the compound inequalities below and solve it graphically. 

Show your graph. 

Explain your process, especially including your use of Test Points.

y > 3x

y < 2x

4. One-half of the boys and one-third of the girls of Fremont High attended the homecoming football game.One-third of the boys and one-half of the girls attended the homecoming dance. If there were 570 students at the game and 580 at the dance, then how many girls and how many boys in total are there at Fremont High?

Define your variables.

Write your equations--both of them.  (You must express this problem as a System of Equations)

Explain your reasoning.

Solve for the number of girls and the number of boys at Fremont High.

5. A chemist wants to mix a 5% acid solution with a 25% acid solution to obtain 50 liters of a 20% acid solution.  How many liters of each of the two starting solutions must she use?

First:  Define your variables--both of them.

Second:  Write your equations--both of them.

Third:  Explain your reasoning.

Fourth:  Solve for the number of liters of each solution.

Show your mathematics.