Question

At the beginning of the year, 1/2 of the seniors at a high school signed up for the debate club. By the end of the year, 7 of the seniors had to quit due to other commitments, leaving 18 members in the club. How many seniors are there at the high school?

Answer 1

Answer: 50

Explanation:

Let the initial number of the senior member at a high school = x

According to the question,

The senior member who signed up for the debate club =
`(x)/(2)`

Thus, When 7 of the seniors had to quit the club, then the remaining number of senior members =
`(x)/(2)-7`

Again according to the question,

`(x)/(2)-7=18`

`\implies (x)/(2)=25`

`\implies x = 50`

Hence, There are 50 senior members at the high school.

Answer 2

There are 50 seniors in the school.

Explanation:

Let the number of seniors in the school = x

It is given that, 'Initially
`(1)/(2)` of the seniors signed up for the club'.

So, the number of seniors in the club =
`(x)/(2)`

Further, 7 seniors left the club at the end of the year and total 18 people were left in the club.

So, we get the relation,

`(x)/(2)-7=18`

i.e.
`(x)/(2)=18+7`

i.e.
`(x)/(2)=25`

i.e. x= 25 × 2

i.e. x = 50

Thus, there are 50 seniors in the school.