Question

15. N MODELING The break-even point is the point at which income equals expenses.Ridgemont High School is paying $13,200 for the writing and research of theiryearbook plus a printing fee of $25 per book. If they sell the books for $40 each, howmany will they have to sell to break even? Explain.

Answer 1

14.

Let:

$\begin{gathered} x=\text{crystal palace tour length} \\ y=\text{horseshoe lake tour length} \end{gathered}$

The total length of both tours is 3.25mi. hence:

$x+y=3.25$

The crystal palace tour is a half-mile less than twice the length of the horseshoe lake tour, so:

$\begin{gathered} x=2y-\frac{1}{2} \\ x=2y-0.5 \end{gathered}$

Now, let:

$\begin{gathered} x+y=3.25\text{ (1)} \\ x=2y-0.5\text{ (2)} \end{gathered}$

Replace (2) into (1):

$\begin{gathered} 2y-0.5+y=3.25 \\ \text{solve for y:} \\ 3y-0.5=3.25 \\ \text{add 0.5 to both sides:} \\ 3y-0.5+0.5=3.25+0.5 \\ 3y=3.75 \\ \text{divide both sides by 3:} \\ y=\frac{3.75}{3} \\ y=1.25 \end{gathered}$

Using elimation:

$\begin{gathered} (1)-(2) \\ x+y-x=3.25-2y-(-0.5) \\ y=3.25-2y+0.5 \\ \text{add 2y to both sides:} \\ 3y=3.75 \\ \text{divide boths sides by 3:} \\ y=\frac{3.75}{3} \\ y=1.25 \end{gathered}$

Replacing the value of y into (2):

$\begin{gathered} x=2y-0.5 \\ x=2(1.25)-0.5 \\ x=2.5-0.5 \\ x=2 \end{gathered}$