Question 77341
The price a flower shop charges for roses is inversely proportional to the number of days before Valentine's Day that the order is placed. A dozen roses ordered ten days before valentine's Day costs $12.00 while the same order placed five days before Valentine's Day costs $24.00. What is the cost of a dozen roses ordered one day before Valentine's day?
:
One way is to write a linear equation by finding the slope and using the
point/slope equation:
:
Let x = number of days from v. day
Then y = cost of the roses on that day
:
x1 = 10, y1 = 12; x2 = 5, y2 = 24
:
Find the slope; m = (y2-y1)/(x2-x1):
:
m = {{{((24-12))/((5-10))}}} = {{{12/-5}}} = -12/5 = -2.4
:
Use the point/slope equation: y - y1 = m(x - x1)
:
y - 12 = -2.4(x - 10)
y - 12 = -2.4x - (-24)
y - 12 = -2.4x + 24
y = -2.4x + 24 + 12
y = -2.4x + 36
;
Substitute 1 for x:
y = 2.4(1) +36
y = $33.60 1 day before v. day