Question

At the first baseball game of the season, every 6th person entering the ballpark received a coupon for a free hot dog. Every 10th person received a coupon for a free soft drink. What is the 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

Answer 1

Answer:

$30\text{th}$

Step-by-step explanation:

GIVEN: At the first baseball game of the season, every $6$ th person entering the ballpark received a coupon for a free hot dog. Every $10$ 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 $6\text{th}$ person receives coupon for free hot dog.

First person who receives coupon for free hot dog$=12\text{th}$

similarly,

next persons who receives coupon for free hot dog$=18\text{th}$$,24\text{th},30\text{th},36\text{th}$

As every $10\text{th}$ person receives coupon for free soft drink.

First person who receives coupon for free hot dog$=20\text{th}$

next persons who receives coupon for free hot dog$=20\text{th},30\text{th},40\text{th}$

As $30\text{th}$ person is common in both.

therefore $30\text{th}$ 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.