# Svetlana's hair is 4 centimeters long. Her hair grows 1.5 centimeters per month. Svetlana wants her hair to grow so that it is at least 7 centimeters long. How many months, m, will it take Svetlana's hair to grow so it is at least 7 centimeters long?

## Write an inequality.

Jul 11, 2017

2 months.

#### Explanation:

first subtract Svetlana present hair length from the desired hair length in order to find out how much growth is required.

$7 - 4 = 3$ so Svetlana needs to grow 3 more cm of hair

Next divide the 3 cm needed to reach the desired length by the rate of growth to find the number of months.

$\frac{3 c m}{\frac{1.5 c m}{m}} = 2 m o n t h s$

Jul 11, 2017

Answer: $m = 2$

#### Explanation:

We are given the current length of hair as $4$ cm and the growth rate of her hair as $1.5$ cm/month. We write a linear inequality to model this problem in the structure of:

$g m + b \ge r$
where $g$ is the slope or growth rate in centimeters, $m$ as our variable for number of months, $b$ is the starting length in centimeters, and $r$ is the required length in centimeters.

Plugging in our values, we have:
$1.5 m + 4 \ge 7$

To find the number of months, $m$, for her hair to grow to be at least $7$ centimeters, we simply solve for $m$:
$1.5 m + 4 \ge 7$

$1.5 m \ge 3$

$m \ge \frac{3}{1.5}$

$m \ge 2$

Therefore, it will take at least 2 months for her hair to be at least 7 centimeters