Question

A company has learned that by pricing a newly released toy at ​$7​, sales will reach 3000 per day. Raising the price to ​$9 will cause the sales to fall to 2000 per day. Assume that the ratio of change in price to change in daily sales is constant and let x be the price of the toy and y be the number of sales.

a. Find the linear equation that models the​ price-sales relationship for this toy.​ [Hint: The line must pass through ​(7​,3000​) and ​(9​,2000​).]

b. Use this equation to predict the daily sales of the toy if the price is set at ​$8.50.

Answer 1

a.

$$slope=m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2000-3000}{9-7}=-500$$

$$y=mx+b$$

Substitute

$$3000=-500(7)+b=>b=6500$$

The linear equation that models the​ price-sales relationship for this toy is

$$y=-500x+6500$$

b. Given $x=\$8.50$

$$y=-500(8.5)+6500$$

$$y=2250$$

The daily sales of the toy will be 2250 per day.