Mohammad went bowling with $50 to spend. He rented shoes for $10.75 and paid $6.25 for each game. What is the greatest number of games Mohammad could play? Write and solve an equation that models this situation and could be used to determine the greatest n of games Mohammad could play.

Let n be the number of games Mohammad can play. We will multiply the price per game by the number of games and add it to the cost of the shoes to create our equation. We will use the ≥ symbol to write our inequality since the total cost must be greater than or equal to the amount spent.

[tex]\displaystyle 50\geq10.75+6.25n[/tex]

Now, we can solve this for n. Subtract 10.75 from both sides of the inequality.

[tex]\displaystyle 39.25 \geq6.25n[/tex]

Divide both sides of the inequality by 6.25.

[tex]\displaystyle 6.28 \geq n[/tex]

Swap the inequality so the variable is on the left side. Since you cannot play 6.28 games, we will round to a total of 6 games.

[tex]\displaystyle n \leq 6.28 \;\text{games}[/tex]