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.

2 Answers
David Drayer
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.

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

Y
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:

#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

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