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?

the 100th, since LCM(20,50) = 100

To find out which customer will be the first to receive both types of gift cards, we need to find the least common multiple (LCM) of 20 and 50.

To calculate the LCM, we can follow these steps:
1. Find the prime factors of each number. Prime factors are the prime numbers that, when multiplied together, give the original number.
- Prime factors of 20: 2, 2, 5 (2 x 2 x 5 = 20)
- Prime factors of 50: 2, 5, 5 (2 x 5 x 5 = 50)
2. Multiply each prime factor the greatest number of times it occurs in either factorization. This gives us the LCM.
- LCM of 20 and 50: 2 x 2 x 5 x 5 = 100

Therefore, the first customer to receive both types of gift cards is the 100th customer.