Question

Your middle school is having a carnival. Admission to the carnival is $8.25 and each game inside the carnival costs $0.50.Part 1: Write an inequality to represent the possible number of games that can be played with $20.75. Let g representthe number of games you play.Part 2: Solve the inequality.Part 3: Is your answer reasonable? Explain why or why not.

Answer 1

Part 1:

`8.25+0.50g\leqslant20.75`

Part 2:

`\begin{gathered} 8.25+0.50g-8.25\le20.75-8.25 \\ (0.50g)/(0.5)\le(12.5)/(0.5) \\ g\leq25 \end{gathered}`

Part 3:

The answer is only reasonable to deduce the maximum number, the interval is not reasonable because it includes negative numbers, which is not possible. The answer is only reasonable if g goes from 0 to 25

Explanation:

Given:

Price per game: $0.5

Admission price: $8.25

If we have a total of $20.75, we establish the following inequality:

`8.25+0.50g\le20.75`

We solve for g:

`\begin{gathered} 8.25+0.50g-8.25\le20.75-8.25 \\ (0.50g)/(0.5)\le(12.5)/(0.5) \\ g\leq25 \end{gathered}`

We graph this:

In other words, that amount of money is limited to 25 games, so the answer makes sense, but if we see it from the graph, we can see that g can take negative values, which does not make sense.

Therefore, it is only reasonable to know the maximum limit, the answer as an interval does not make sense.