a music 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?
20, 40, 60, 80, 100, 120, 140
50, 100, 150, 200
20=2*2*5
50=2*5*5
the first customer to receive both = 2*2*5*5=100 - that would be the smallest common multiple
100
To find the customer who will be the first to receive both types of gift cards, we need to determine the least common multiple (LCM) of 20 and 50. The LCM is the smallest multiple that both numbers evenly divide into.
1. Start by listing the multiples of each number:
- Multiples of 20: 20, 40, 60, 80, 100, ...
- Multiples of 50: 50, 100, 150, 200, ...
2. Look for the first common multiple in these lists. We find that both 100 and 200 are common multiples.
Therefore, the first customer to receive both types of gift cards will be the 100th customer.