Question

Mrs. Zabel, the yearbook adviser, always likes to sell a large amount of yearbooks because after the initial set-up costs are paid, the printing is not too expensive.

If the yearbook staff sells 50 yearbooks, the cost per yearbook is $45. If they sell 125 yearbooks, the cost per yearbook is $37.50.

Assuming a linear equation fits the situation, find the price per yearbook if the staff sells 150 yearbooks.

Answer 1

imagine a graph where the x-axis is the number of books sold, and the y-axis is the price per book. You could make such a graph by plotting the points (50,$45), (125,$37.50) and drawing a straight line through them. Graphically, you could then read off the price per yearbook by going to 150 on the x-axis and finding the value of y at that point.

Algebraically, you need to write the equation for a line passing through those two points. Use the slope formula to find the slope \((m)\):
\[m = \frac{y_2-y_1}{x_2-x_1}\]and then use the point-slope formula to construct the formula for the line with slope \(m\) passing through point \((50,45)\) or \((125,37.50)\):
\[y-y_0 = m(x-x_0)\]
Finally, rearrange the equation to solve for \(y\) and evaluate \(y\) when \(x = 150\).