Question

if a large Factory sells its new gadgets for $5 each it can sell 1050 per month if it sells the same gadgets for $9 it will sell 900 per month assuming the relationship between prices and sales is linear predict the monthly sales of gadgets to the nearest whole number if the price is $12

Answer 1

you are given 2 ordered pairs

(5 , 1050) and (9,900)

slope = (900 - 1050)/(9-5) = - 150/4 = - 75/2

N = (-75/2)C + b

using (5,1050)

1050 = (-75/2)(5) + b

1050 + 375/2 = b

b = 2475/2

N = (-75/2)C + 2475/2 or N = -37.5C + 1237.5

where N is the number sold and C is the price of each

so when C = 12

N = -37.5(12) + 1237.5 = 787.5

number sold = 788

Explanation:

Answer 2

788 Since we're assuming a linear relationship between sales and price, let's create an equation for the two points that we know. The general form of the equation will be in slope intercept form, so s = ap + b where s = number of sales a = slope of line p = price b = y intercept. So let's calculate a first. a = (1050 - 900)/(5-9) a = 150/(-4) a = -150/4 a = -37.5 So we now have the equation s = -37.5p + b Let's substitute one of out known price, sales pairs and solve for b. s = -37.5p + b 1050 = -187.5 + b 1237.5 = b So now we have the equation: s = -37.5p + 1237.5 Finally, just plug in the value 12 for p and calculate s. s = -37.5p + 1237.5 s = -37.5*12 + 1237.5 s = -450 + 1237.5 s = 787.5 And after rounding to the nearest whole number, we get 788.