Question

A furniture store is having a going-out-of-business sale. Two hours after opening, there are 415 sofas still available. Three hours later, there are 301 sofas available. How many hours will the store have to stay open to sell the entire inventory? Assume the sales rate is constant and round your answer to the nearest whole hour.

Answer 1

Because the sales rate is constant, assume that
x(t) = a + bt
where
x = number of sofas remaining after t hours from opening,
a, b are constants.

When t = 2 hours, x = 415. Therefore
a + 2b = 415 (1)

Three hours later (t = 2 +3 = 5), there are 301 sofas left.
Therefore
a + 5b = 301 (2)

Subtract (2) from (1).
-3b = 415 - 301 = 114
b = -38

From (1), obtain
a = 415 - 2*(-38) = 491

The required function is
x(t) = 491 - 38t

When all sofas are sold, x=0. Therefore the time required to complete the sale is given by
491 - 38t = 0
38t = 491
t = 12.92 hours

Answer:
The time required to sell the inventory is 13 hours (nearest whole hour)