Answer:
![30\text{th}](https://tex.z-dn.net/?f=30%5Ctext%7Bth%7D)
Step-by-step explanation:
GIVEN: At the first baseball game of the season, every
th person entering the ballpark received a coupon for a free hot dog. Every
th person received a coupon for a free soft drink.
TO FIND: number of the first person to enter the ballpark that received a coupon for a free hot dog and a coupon for a free soft drink.
SOLUTION:
As every
person receives coupon for free hot dog.
First person who receives coupon for free hot dog![=12\text{th}](https://tex.z-dn.net/?f=%3D12%5Ctext%7Bth%7D)
similarly,
next persons who receives coupon for free hot dog![=18\text{th}](https://tex.z-dn.net/?f=%3D18%5Ctext%7Bth%7D)
![,24\text{th},30\text{th},36\text{th}](https://tex.z-dn.net/?f=%2C24%5Ctext%7Bth%7D%2C30%5Ctext%7Bth%7D%2C36%5Ctext%7Bth%7D)
As every
person receives coupon for free soft drink.
First person who receives coupon for free hot dog![=20\text{th}](https://tex.z-dn.net/?f=%3D20%5Ctext%7Bth%7D)
next persons who receives coupon for free hot dog![=20\text{th},30\text{th},40\text{th}](https://tex.z-dn.net/?f=%3D20%5Ctext%7Bth%7D%2C30%5Ctext%7Bth%7D%2C40%5Ctext%7Bth%7D)
As
person is common in both.
therefore
person is the first person to enter ballpark that received a coupon for a free hot dog and a coupon for a free soft drink.