Question

A gamer room charges a 13 entrance fee, plus $ 2.35$ per hour of play hour of play time. Anne-Marie has 29.45. For how long can she play in the games room? Choose a variable and write an inequality for this problem.

Answer 1

Hint: We will first assume that the number of hours she plays and then multiply that by 2.35. Then, we will add 13 to it and equate it less than or equal to 29.45 and get an inequality for the number of hours.

Complete step-by-step answer:
Let us assume that she plays for $x$ hours.
Now, since we are already given the question that the entry fee is $ 13$.
So, as she enters, she already pays $ 13$.
We are also given that playing 1 hour would cost her $ 2.35.$
So, playing $x$ hours would cost her $2.35x$.
So, her total cost would be playing fee + the entrance fee.
Hence, total cost = $2.35x + 13$.
She has in all $ 29.45.$
Hence, here total cost should be less than or equal to the money she has.
Hence, $2.35x + 13 \leqslant 29.45$
Taking the 13 from LHS to RHS, we will get:-
$ \Rightarrow 2.35x \leqslant 29.45 - 13$
On simplifying the RHS, we will get:-
$ \Rightarrow 2.35x \leqslant 16.45$
Now taking the 2.35 from LHS to RHS, we will get:-
$ \Rightarrow x \leqslant \dfrac{{16.45}}{{2.35}}$
On simplifying the RHS, we will get:-
$ \Rightarrow x \leqslant 7$

Hence, she can play at maximum for 7 hours with the amount of money she has with her.

Note: The students might make the mistake of forgetting the entrance fee which will vary their answer.
There is one more way to solve this as well. First, charge her the entrance fees and subtract it from the money she has and then equate the playing hours with the leftover money and you will get the answer.
Always remember that you may add any positive or negative number to both sides of an inequality. You may multiply or divide both sides of an inequality by any positive number.