Question

Sofie makes and sells scarves. Her profit depends on what price she charges for a scarf.

She writes the expression (x−5)(50−2x)
to represent her profit based on the price per scarf, x
.

Enter Sofie's average change in profit for two different sections of the graph.


A graph has price per scarf (dollars) on the x-axis, and profit (dollars) on the y-axis. A parabola with equation f (x) = (x minus 5) (50 minus 2 x) opens down and goes through (5, 0), has vertex (15, 200), and goes through (25, 0).
CLEAR CHECK
What is Sofie's average change in profit from x=5
to x=15
?

For every $1
increase in the price per scarf, Sofie's profit changes by an average of $
.

What is Sofie's average change in profit from x=15
to x=25
?

For every $1
increase in the price per scarf, Sofie's profit changes by an average of $
.​

Answer 1

To find Sofie's average change in profit for two different sections of the graph, we can use the formula:

Average change in profit = (change in profit) / (change in price)

First, let's find Sofie's average change in profit from x=5 to x=15:

- At x=5, Sofie's profit is 0.
- At x=15, Sofie's profit is 200 (the vertex of the parabola).
- The change in profit is 200 - 0 = 200.
- The change in price is 15 - 5 = 10.
- Therefore, the average change in profit is 200 / 10 = $20.

So, for every $1 increase in the price per scarf from $5 to $15, Sofie's profit changes by an average of $20.

Next, let's find Sofie's average change in profit from x=15 to x=25:

- At x=15, Sofie's profit is 200 (the vertex of the parabola).
- At x=25, Sofie's profit is 0.
- The change in profit is 0 - 200 = -200.
- The change in price is 25 - 15 = 10.
- Therefore, the average change in profit is -200 / 10 = -$20.

So, for every $1 increase in the price per scarf from $15 to $25, Sofie's profit changes by an average of -$20 (or a decrease of $20).