Question

Rebecca's hair is 3 inches long. Her hair grows 2 inches every month. She wants her hair to be at most 9 inches. Can she go for 4 months without a haircut?

• A. No. She can not wait for $4\text{months}$ without a haircut.
• B. Yes. She can can go for $4\text{months}$ without a haircut.

Answer 1

The correct option is A No. She can not wait for $4\text{months}$ without a haircut.

Let $x$ indicates the number of months she can go without cutting her hair.

Her hair grows 2 inches per month.
$\therefore$ In $x$ number of months, her hair will grow by $2\times x=2x\text{inches.}$

Initially, her hair is 3 inches long.
After $x$ months, her hair length will be $3+2x\text{inches.}$

Rebecca wants her hair to be at most 9 inches.
$\therefore$ Her hair length should be less than or equal to $9\text{inches.}$
$\Rightarrow 3+2x\le 9$

Step 1: To solve this equation we first subtract $3$ from both side of the inequality.

$3+2x\le 9-3=-32x\le 6$

Step 2: Divide both side of the inequality by $2$.
$2x\le 6$
$\Rightarrow \frac{2x}{2}\le \frac{6}{2}$
$\Rightarrow x\le 3$

$\therefore x$ should be less than or equal to $3\text{months}$ to make sure that her hair does not grow beyond $9\text{inches.}$

Hence, she can not wait for $4\text{months}$ without a haircut.