6. A store is giving away a $10 coupon to every 7th person to enter the store and a $25 coupon to every 18th person to enter the store. Which person will be the first to get both coupons
To find the person who will be the first to get both coupons, we need to determine the least common multiple (LCM) of 7 and 18. The LCM is the smallest number that is divisible by both 7 and 18.
To find the LCM, we can list the multiples of each number until we find a common multiple:
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, ...
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, ...
From the lists above, we can see that 126 is the first number that is divisible by both 7 and 18.
Therefore, the person who will be the first to get both coupons is the 126th person to enter the store.