Amusic store gives every 20th customer a $5 gift card. every 50th customer gets a $10 gift card. which customer will be the first to receive both types of gift cards?

The correct answer of the given question above would be the 100th customer.
Since it is stated that every 20th customer gets a $5 gift card, so its the 20th, 40ths, 60th, 80th and the 100th customers. Next, it is said that every 50th customer gets a $10 gift card so it is the 50th and next is the 100th customer. Notice that with both customers, it is the 100th customer who receives both of the gift cards. Hope this answer helps.