Final answer:
To write an inequality to show how many cards Gerardo has, assign variable x to Gerardo's cards. Then, write the inequality x + (x/2) + 20 ≥ 350. Simplify and solve to find that Gerardo must have at least 220 cards.
Step-by-step explanation:
To write an inequality to show how many cards Gerardo has, let's start by assigning a variable. Let's say Gerardo has 'x' cards. According to the given information, Louie has 20 more than half as many cards as Gerardo. So, Louie has (x/2) + 20 cards.
Together, they have at least 350 cards. So, the combined number of cards will be Gerardo's cards plus Louie's cards, which is x + (x/2) + 20. This sum should be greater than or equal to 350.
Therefore, the inequality that represents the situation is: x + (x/2) + 20 ≥ 350.
To solve this inequality, we can simplify it: 2x + x + 40 ≥ 700. Combining like terms, we get 3x + 40 ≥ 700. Subtracting 40 from both sides, we get 3x ≥ 660. Finally, dividing both sides by 3, we find that x ≥ 220.
So, Gerardo must have at least 220 cards.