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

`30\text{th}`

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.