1. ## quadratic equations

1)Rs,6500 were divided equally among a certain number of persons.if there had been 15 more person,each would have got Rs.30 less,find the original number of persons?

2. Originally Posted by anjana
1)Rs,6500 were divided equally among a certain number of persons.if there had been 15 more person,each would have got Rs.30 less,find the original number of persons?
write it out into an equation: $\frac{6500}{p}=n$

now write out the second equation: $\frac{6500}{p+15}=n-30\quad\Rightarrow\quad\frac{6500}{p+15}+30=n$

therefore: $\frac{6500}{p}=\frac{6500}{p+15}+30$

Multiply both sides by "p+15" $\frac{6500p+97500}{p}=6500+30p+450$

multiply both sides by p: $6500p+97500=6500p+30p^2+450p$

move everything to one side: $-30p^2+6500p-6500p-450p+97500=0$

subtract: $-30p^2-450p+97500=0$

and now you can use the quadratic formula (I hope you know how to do that)

3. I might as well continue:

using the quadratic formula you get: $p=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

substitute: $p=\frac{-(-450)\pm\sqrt{(-450)^2-4(-30)(97500)}}{2(-30)}$

multiply: $p=\frac{450\pm\sqrt{202500+11700000}}{-60}$

add: $p=\frac{450\pm\sqrt{11902500}}{-60}$

find sqrt: $p=\frac{450\pm3450}{-60}$

split equation: $p=\left\{\begin{array}{cc}(450-3450)\div-60=-3000\div-60=50\\(450+3450)\div-60=3900\div-60=-65\end{array}\left$

therefore, after throwing away the negative answer, there were 50 people