Question

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.

Answer 1

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.

`(3 cm)/ { (1.5cm)/m)= 2 months`

Answer 2

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:

`gm+b>=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:
`1.5m+4>=7`

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

`1.5m>=3`

`m>=3/1.5`

`m>=2`

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