Question

a blind state test is over and a new favorite juice flavor has been selected. The new flavor received 5 votes for every vote received by the original flavor. the new flavor received 705 votes. how many votes did the original flavor receive?

Answer 1

Let the number of votes received by the original flavor be x and let the votes received by the new flavor be y:

Since, for every vote received by the original flavor, 5 votes are received by the new flavor. It follows that the number of votes received by the new flavor is 5 times the number of votes received by the original flavor. That is:

$y=5x$

Substitute the number of votes y=705 votes for the new flavor into the equation and solve for x:

$\begin{gathered} 705=5x \\ \text{Swap the sides of the equation:} \\ \Rightarrow5x=705 \\ \Rightarrow\frac{5x}{5}=\frac{705}{5} \\ \Rightarrow x=141\text{ votes} \end{gathered}$

Hence, the number of votes the original flavor receive