Problema Solution
In 2005, the members of a club paid a total of $42 in subscription fees.In 2006,the number of members increased by 20 and the subscription fees were subsequently reduced by 10 cents per member. the total of the subscription fees for 2006 was $45. How many members were there in 2005?
Answer provided by our tutors
Let x be the number of members in 2005 and r the rate per head.. Then the total subscription of 2005 = 45.
The members in 2006 =x+20 and their contribution after 10% reduction of rate of subscription = (x+20)r*(90%) =42.
Therefore the equations to be solved is xr=45. (1) and
(x+20) r*0.9=42. (2).
From (1) and (2) we get xr+20r = 45+20r= 42/0.9 .
Therefore, 20r = 42/.9-45 = 140/3-45 =5/3.
Therefore, r =5/60 = 1/12.
Therefore, from (1), x(1/12) =45 or x= 45*12 = 540. Which is the number of members in 2005.
Tally:540*1/12 =45.
(540+20)(1/12)(0.9) =42.