Answer :
Answer:
[tex]30\text{th}[/tex]
Step-by-step explanation:
GIVEN: At the first baseball game of the season, every [tex]6[/tex] th person entering the ballpark received a coupon for a free hot dog. Every [tex]10[/tex] 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 [tex]6\text{th}[/tex] person receives coupon for free hot dog.
First person who receives coupon for free hot dog[tex]=12\text{th}[/tex]
similarly,
next persons who receives coupon for free hot dog[tex]=18\text{th}[/tex][tex],24\text{th},30\text{th},36\text{th}[/tex]
As every [tex]10\text{th}[/tex] person receives coupon for free soft drink.
First person who receives coupon for free hot dog[tex]=20\text{th}[/tex]
next persons who receives coupon for free hot dog[tex]=20\text{th},30\text{th},40\text{th}[/tex]
As [tex]30\text{th}[/tex] person is common in both.
therefore [tex]30\text{th}[/tex] 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.