Respuesta :
Percentage of the votes did John got overall is 25 %
Solution:
Given, Vivenne, John and nassim ran for 6th grade class president.
Vivenne got four votes for every 3 votes that John got.
Nassim got two votes for every vote that Vivenne got.
Now, ratio of vivenne votes to john votes = 4 : 3
a : b can be written in fraction as [tex]\frac{a}{b}[/tex]
[tex]\rightarrow \frac{\text {vivenne votes}}{\text {john votes}}=\frac{4}{3} \rightarrow(1)[/tex]
Now, ratio of nassim votes to vivenne votes = 2 : 1
[tex]\rightarrow \frac{\text {nassim votes}}{\text {vivenne votes}}=\frac{2}{1} \rightarrow(2)[/tex]
Now, multiply the above two fractions,
[tex]\begin{array}{l}{\rightarrow \frac{\text {vivenne votes}}{\text {john votes}} \times \frac{\text {nassim votes}}{\text {vivenne votes}}=\frac{4}{3} \times \frac{2}{1}} \\\\ {\rightarrow \frac{\text {nassim votes}}{\text {john votes}}=\frac{8}{3} \rightarrow(3)}\end{array}[/tex]
Now, add (1) and (3),
[tex]\begin{array}{l}{\rightarrow \frac{\text {vivenne votes}}{\text {john votes}}+\frac{\text {nassim votes}}{\text {john votes}}=\frac{4}{3}+\frac{\mathrm{s}}{3}} \\\\ {\rightarrow \frac{\text {vivenne votes+nassim votes}}{\text {john votes}}=\frac{4+8}{3}}\end{array}[/tex]
We know that total votes = vivenne votes+nassim votes+john votes
Hence substitute "vivenne votes+nassim votes = total votes - john votes "
Hence we get,
[tex]\begin{array}{l}{\rightarrow \frac{\text {total votes}-\text {john votes}}{\text {john votes}}=\frac{12}{3}} \\\\ {\rightarrow \frac{\text {total votes}}{\text {john votes}}-\frac{\text {john votes}}{\text {john votes}}=4} \\\\ {\rightarrow \frac{\text {total votes}}{\text {john votes}}-1=4} \\\\ {\rightarrow \frac{\text {total votes}}{\text {john votes}}=5} \\\\ {\rightarrow \frac{\text {john votes}}{\text {total votes}}=\frac{1}{5}}\end{array}[/tex]
Multiplying 100 on both sides,
[tex]\rightarrow \frac{\text {john votes}}{\text {total votes}} \times 100=\frac{1}{5} \times 100[/tex]
The above expression is the formula used to calculate John vote percentage
Hence John votes percentage = 25%
