Question

Rachel used 3/8 of her money to buy some blouses and 2/5 of the remainder to buy 2 pair of pants. A pair of pants costs 3 times as much as a blouse. How many blouses did she buy?

Answer 1

The answer is: 9 blouses.

The explanation is shown below:

1. The remainder is:

$1-\frac{3}{8}=\frac{5}{8}$

2. She used $\frac{2}{5}$ of the remainder to buy 2 pair of pants:

$(\frac{5}{8})(\frac{2}{5})=\frac{1}{4}$

3. Then, she used $\frac{1}{4}$ of the money to buy 2 pairs of pants. For each one she used:

$\frac{1}{4}$÷$2$=$\frac{1}{8}$ of the money for a pair of pants.

4.  A pair of pants costs 3 times as much as a blouse, therefore you can write the following expression:

$\frac{1}{8}=3x$

Where $x$ is the cost of 1 blouse

5. Solve for $x$:

$x=\frac{1}{24}$ for each blouse

6. If she used $\frac{1}{24}$ of the money for 1 blouse, you have the following amount of blouses bought with $\frac{3}{8}$ of the money:

$y=\frac{\frac{3}{8}}{\frac{1}{24}}=9$

Where $y$ is the total number of blouses.