Question 1011171
Members of a boating club were assessed equally to raise $600 to pay for a new set of sails. When six more persons joined the club, the per member assessment was reduced by $5.00. What was the new size of the club?
<pre>Let new size be M
Then original size = M - 6
Now, each member pays: {{{600/M)}}}, and originally, each member paid: {{{600/(M - 6)}}}
We then get the following equation, which describes the per-member payment, now and before: {{{600/M = 600/(M - 6) - 5}}}
600(M - 6) = 600M - 5M(M - 6) --------- Multiplying by LCD, M(M - 6)
{{{600M - 3600 = 600M - 5M^2 + 30M}}}
{{{5M^2 - 600M - 30M + 600M - 3600 = 0}}}
{{{5M^2 - 30M - 3600 = 0}}}
{{{5(M^2 - 6M - 720) = 5(0)}}}
{{{M^2 - 6M - 720 = 0}}}
(M - 30)(M + 24) = 0
M, or new size  = {{{highlight_green(30)}}}           OR         M = - 24 (ignore)