Final answer:
To determine the most games Carl can play at the arcade, we created the inequality 1.75G <= 18, which leads to the solution G <= 10.2857. As Carl cannot play a fraction of a game, the maximum number of games he can play is 10.
Step-by-step explanation:
To find the most number of games Carl can play at the arcade, we need to establish an inequality reflecting his budget after spending money on food. Carl has $30 and spends $12 on food, leaving him $18 for games. Each game costs $1.75.
Let's define G as the number of games Carl can play. We can create the following inequality for his budget constraint:
1.75G ≤ 18
To solve for G, divide both sides of the inequality by 1.75:
G ≤ 18/1.75
G ≤ 10.2857
Since Carl can't play a fraction of a game, we round down to the nearest whole number, which gives us:
G ≤ 10
Therefore, the most number of games Carl can play is 10 games.