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
Accepted Solution
A:
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.