Problem Solving

Princeton Review

A department store receives a shipment of 1,000 shirts, for which it pays $9,000. The store sells the shirts at a price 80 percent above cost for one month, after which it reduces the price of the shirts to 20 percent above cost. The store sells 75 percent of the shirts during the first month and 50 percent of the remaining shirts afterward. How much gross income did sales of the shirts generate?

A. $10,000
B. $10,800
C. $12,150
D. $13,500
E. $16,200

OA D.

Store receives 1000 shirts and pays $9000
$$1\ shirt=\frac{$9000}{1000}=$9$$

For 1 month, the store sells 80% above the cost.
Selling price of 1 shirt for 1 month = [80% of $9] + $9
$$=\left[\frac{80}{100}\cdot9\right]+9$$
$$=7.2+9$$
$$=$16.2$$
Thus, 75% of the shirts were sold in the first month.
$$i.e\ 75\%\ of\ 1000\ =\ \frac{75}{100}\cdot1000=750$$
$$So,\ 750shirts\ were\ sold\ for\ =\ $16.2\cdot750$$
$$=\ $12150$$
After this month, the store sells the shirt at 20% above the cost.
Selling price of 1 shirt now become = [20% of $9] + $9
$$\left[\frac{20}{100}\cdot$9\right]+9$$ $$ $1.8+$9= $10.8$$

50% of the remaining shirts were sold during this period.
Remaining shirt = 1000 - 750 =250
$$50\%\ of\ 250\ =\ \frac{50}{100}\cdot250\ =125shirts$$
125 shirts were sold for = $10.8 x 125 = $1.350

Therefore, Total gross income income = $12,150 + $1,350
$$=$13,500$$