Question

At a two-hour basketball practice, Tracy can either choose to run miles, which take six minutes per mile, or play scrimmage games, which take 30 minutes per game. If Tracy cannot run more than five miles in any given practice, which system of inequalities describes the feasible number of miles she can run (m) and the number of scrimmages she can play (s) in a given practice?

Answer 1

See the image attachment. It shows the three inequalities

`6m+30s \le 120`

`0 \le m \le 5`

`s \ge 0`

the inequalities are all stacked on each other with a large curly brace written off to the left

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Step-by-step explanation:

Let,

m = number of miles Tracy runs

s = number of scrimmage games Tracy plays

m and s are integers

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Each mile takes 6 minutes, so running m miles takes up a total of 6m minutes.

Each scrimmage game takes 30 minutes, so in total she uses up 30s minutes of time if the number of games she plays is 's'.

In total, Tracy uses up 6m+30s minutes running and playing scrimmage games. The max time allotted for her is 2 hours or 120 minutes. Therefore,
`6m+30s \le 120` is one inequality that makes up the system of inequalities.

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We know that 'm' is positive, and we also know that m cannot get larger than 5, so we can write
`0 \le m \le 5`. This says "m is between 0 and 5 including both endpoints".

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For similar reasons in the last section above, we also know that 's' is positive as well; however we have no upper bound restrictions on 's'. So we simply say
`s \ge 0`

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Overall, the system of inequalities has these three inequalities:

`6m+30s \le 120`

`0 \le m \le 5`

`s \ge 0`

they are all stacked on each other and written with a large curly brace to the left hand side of this stack. The large curly brace is just a way of keeping things together in a group or collection so to speak. A paired right curly brace is not included.

A visual reference of the answer is attached as an image below, just so you can see what I mean by the large curly brace.