49 red, 1 green in same jar, how many red to add to get 99%?

[smart_pirate]

if there are 49 red jelly beans and 1 green jelly bean in the same jar, how many red jelly beans would you have to add to the jar to get from 98% to 99% ?

i need help and cant figure it out

 

[Loren]

Re: help!!!

I guess the 1 green jellybean represents 1% of the total number of jellybeans? So, 1 is 1% of how many as the total? So how many green ones are there?

 

[soroban]

Hello, smart_pirate!

If there are 49 red jelly beans and 1 green jelly bean in the same jar,
how many red jelly beans would you have to add to the jar to get from 98% red to 99% red?

If we must use algebra to solve it . . .


\(\displaystyle \text{At the start, we have: }\;\begin{array}{|c|c|} \hline \text{color} & \text{count} \\ \hline\hline \text{Red} & 49 \\ \hline \text{Green} & 1 \\ \hline\hline \text{Total:} & 50 \\ \hline \end{array}\)

. . \(\displaystyle \text{Percent red} \:=\:\frac{49}{50} \:=\:0.98 \:=\:98\%\)


\(\displaystyle \text{We add }R\text{ red jelly beans: }\;\;\begin{array}{|c|c|} \hline \text{color} & \text{count} \\ \hline\hline \text{Red} & 49 +R \\ \hline \text{Green} & 1 \\ \hline\hline \text{Total: } & 50+R \\ \hline \end{array}\)

\(\displaystyle \text{Percent red will be 99\%.}\)

. . \(\displaystyle \text{We have: }\:\frac{49+R}{50+R} \:=\:\frac{99}{100} \quad\Rightarrow\quad 4900 + 100R \:=\:4950 + 99R \quad\Rightarrow\quad R \:=\:50\)


Therefore, 50 red jelly beans must be added.