Question

In a specific video game scenario, you are given 1,000 gold. You can either train marines to defend your base at 50 gold a piece or research weapon upgrades at 200 gold per upgrade. The game allows a maximum of three upgrades, and you know that you need at least ten marines trained to survive the next level. Which of the following systems correctly describe the number of marines (m) and the number of upgrades (u) you can train/purchase in the game?

Answer 1

Answer:

The system is:

                $50m+200u\leq 1,000$

                 $u\leq 3$

                 $u\geq 0$

                 $m\geq 10$

Step-by-step explanation:

The variables of your equations are:

       $m=\text{number of marines}$

       $u=\text{number of upgrades}$

The constraints, which become inequalities are:

1. The total cost cannot be greater than 1,000 gold

• Cost of training m number of marines at 50 gold a piece:

               $50m$

• Cost of purchasing u number of research weapon upgrades at 200 gold per upgrade:

                $200u$

• Total cost:

                $50m+200u$

• The cost is limited to 1,000 gold that you are given:

                $50m+200u\leq 1,000$

          That is the first inequality of your system

2. The game allows a maximum of three upgrades:

• This sets an upper bound for the variable:

                   $u\leq 3$

• Add the reasonable constraint that the number of upgrades cannot no be negative:

                   $u\geq 0$

3. You know that you need at least ten marines trained to survive

• This sets a lower bound for the variable:

                  $m\geq 10$

And those are all the four inequalities that form your system to describe the number of marines and the number of upgrades you can train/purchae in the game:

                $50m+200u\leq 1,000$

                 $u\leq 3$

                 $u\geq 0$

                 $m\geq 10$