Jameschan168 wrote:A certain business produced x rakes each month from November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.10 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business for the rakes for the 12 month from November through October?

a. 0.40x
b. 1.20x
c. 1.40x
d. 1.60x
e. 3.20x

In the 4 months leading up to March, the company PRODUCES 4x rakes (4 months at x/month = 4x)

On March 1, x/2 rakes are SHIPPED, leaving 3.5x rakes for which the company must pay storage fees.
On April 1, x/2 rakes are SHIPPED, leaving 3x rakes for which the company must pay storage fees.
On May 1, x/2 rakes are SHIPPED, leaving 2.5x rakes for which the company must pay storage fees.
etc... (this pattern continues until no rakes remain).

The total NUMBER of rakes (for which storage fees are paid) = 3.5x + 3x + 2.5x . . . + 1x + 0.5x
= 14x

The charge is $0.1/rake, so the total FEE = (0.1)(14x) = 1.4x

Answer: C

Cheers,
Brent

Jameschan168 wrote:A certain business produced x rakes each month from November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.10 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business for the rakes for the 12 month from November through October?

a. 0.40x
b. 1.20x
c. 1.40x
d. 1.60x
e. 3.20x

We know that the business didn't need to pay storage costs from November to February. So let's begin by analyzing what happened in March. Just before March, the business had 4x rakes, and at the beginning of March, they shipped out x/2 rakes; therefore, for the month of March, they had 4x - x/2 = 8x/2 - x/2 = 7x/2 rakes that required storage costs of $0.10 each.

Since they shipped out x/2 rakes at the beginning of each of the subsequent months, from April to October, the number of rakes in storage in these months are 6x/2, 5x/2, 4x/2, 3x/2, 2x/2, x/2 and 0, respectively. Including the 7x/2 rakes in March, the total number of rakes that require storage costs is:

(7x/2 + 0)/2 * 8 = 7x/2 * 4 = 14x

Since each rake cost $0.10 to store, the total storage costs are 14x * 0.1 = 1.4x dollars.

Answer: C