Question

Rebecca's hair is 3 inches long. Her hair grows at the rate of 0.5 inches per month. She wants her hair to be no longer than 9 inches. What is the maximum time period (in months) she can stay without a haircut?

• A. 9 months
• B. 5 months
• C. 7 months
• D. 12 months

Answer 1

The correct option is D 12 months

Let $x$ be the number of months she can go without a haircut.

Rate of hair growth = 0.5 in per month
In $x$ months, Rebecca’s hair will grow by$0.5\times x=0.5x$ in
Initial length of her hair = 3 in
After $x$ months, the length of her hair will be $(3+0.5x)$ in.

Rebecca wants her hair to be no longer than 9 in, i.e., her hair length should be less than or equal to 9 in.
$\Rightarrow 3+0.5x\le 9$

Step 1: Subtract 3 from both sides of the inequality to solve it. $0.5x\le 9-3=6$

Step 2: Multiply both sides by 2.
$\Rightarrow x\le 6\times 2$
$\Rightarrow x\le 12$
Therefore, $x$ should be less than or equal to 12, i.e., Rebecca can stay 12 months without a haircut until her hair grows longer than 9 in.