Math homework help

Question

A company hass learned that by pricing newly released toys at 7$,, salles will reach 2,500 A day. Raising the prices to 9$ will cause the sales to fall to 2,000 per day, Assume the ratio of change in price to change in daily sales is constant.

A.) Find the linear equation that models the price-sales relationship for this toy and

B.) Use the equation to predict the daily sales of the toy if the price is set at 7.50$

Answer 1

9-7 =$2 price increase means 2500-2000 = 500 decrease in sales

$1 increase means 500/2 = 250 decrease in sales

50 cents increase has 125 decrease

at 7+.5 = $7.50, 2500-125

= 2,375 sold at $7.50

q = -250p + b, to solve for b, plug in (q,p) = (2500, 7)

2500 =-250(7) + b

b= 2500+1750

=4250

= how many people take when it's free

b= the x intercept

q= -250p+4,250 is the linear equation

at $7.50 quantity sold =

q= -250(7.5)+4250

=-1875+4250

=2,375