Question

3 A new club opens with 20 members, plus an unknown number of members from another club. The club allows only members to join once a year. After the first year, the number of total members doubles. The following year, half of the members that joined from the other club leave, but another 40 people join. After the third year, the total number of members triples. Give a non-simplified expression that represents the total number of members at the club after the third year. Then simplify your expression ​

Answer 1

Explanation:

let the unknown members be X

At first, the club had 20 + X members

After the first year,

2( 20+X)

The second year,

2( 20 +X/2) +40

The third year,

3[2(20+ X/2) +40]

Total number =

20+X + 2(20+X) + 2( 20 +X/2) +40 +3[2(20+ X/2) +40]

= 20+ X + 40+ 2X + 40 +2X/2 +40 +3[40+2X/2 +40]

= 20+40+X +2X +40+X+ 40 + 3[ 40+40+X]

= 60 +3X +80+X + 3[80+X]

= 140+4X + 240+3X

=380 + 7X

-380=7X

X = -54.3