Chapter 4.6, Problem 46HP

To determine

To calculate: the number of girls and boys voted.

Answer to Problem 46HP

Option D is correct..

Explanation of Solution

Given information:

A night under the stars received 225 votes

The time of my life received 480 votes

40% of girls voted for “a night under the stars” and 75% of boys voted for “ the time of my life”

Formula used:

Substitution is used.

Calculation:

Consider,

Let the x be the number of votes voted by boys.

Let the y be the number of votes voted by girls.

According to the question,

  $\begin{array}{l}0.25x+0.4y=225\\ 0.75x+0.6y=480\end{array}$

Multiplying equation first by 3 and subtract the second equation

  $\begin{array}{l}=(3\times 0.25x)+(3\times 0.4y)=(3\times 225)\\ =0.75x+1.2y=675\end{array}$

  $\begin{array}{l}=(0.75x+1.2y)-(0.75x+0.6y)=675-480\\ =0.75x+1.2y-0.75x-0.6y=675-480\\ =0.6y=195\\ =\frac{0.6y}{0.6}=\frac{195}{0.6}\\ =y=325\end{array}$

Substituting value of y in equation first

  $\begin{array}{l}=0.25x+0.4(325)=225\\ =0.25x+130=225\\ =0.25x=225-130\\ =0.25x=95\\ =\frac{0.25x}{0.25}=\frac{95}{0.25}\\ =x=380\end{array}$

Therefore, the number boys are 380 and girls are 325.