please help me i've been stuck on this question forever

Question

Write a system of equations to describe the situation below, solve, and write as an ordered pair (with number of months as x). Two friends, Ann and Malia, are growing out their hair. They plan to cut it off at a certain point and donate it to a charity that makes wigs for people with cancer. Ann's hair is already 23 centimeters long and grows at a constant rate of 3 centimeters per month. Malia's hair is 27 centimeters and growing at a speed of 1 centimeter per month. If the girls get their hair cut on a certain day, they will have exactly the same length to donate. How long will their hair be? How long will that take?

Answer 1

Ann's hair length: y = 23 + 3x

Malia's hair length: y = 27 + x

Thus: 23 + 3x = 27 + x

23 + 2x = 27

2x = 4

x = 2

Ann's hair length: y = 23 + 2(3) = 29

Malia's Hair length: y = 27 + 2 = 29

Solution: (x, y) = (2, 29)

In 2 months both Ann's and Malia's hair will be 29 centimeters long.

Answer 2

Answer 3

First, define the variables.

Let x = the number of months they are growing their hair.

Let y = hair length

Ann's hair is already 23 centimeters long and grows at a constant rate of 3 centimeters per month.

This would be:

y=23+3x

Malia's hair is 27 centimeters and growing at a speed of 1 centimeter per month.

This would be:

y=27+1x

To find out when they are equal, set the equations equal to each other (This is solving by substitution)

23+3x=27+1x Subtract x from both sides

23+2x=27 Subtract 23 from both sides

2x=4 Divide by 2

x=2 It will take 2 months for their hair to be equal length.

Next, solve for y using either equation

y=27+1(2)

y=29 Their hair will be 29 inches

Answer 4

Let's start with Ann's hair: 23 centimeters + 3 centimeters per month

Malia's hair: 27 centimeters + 1 centimeter per month

Now we can substitute the number of months for "x"

Ann's hair length = 23 + 3x

Malia's hair length = 27 +1x

We know that we want both girls to have the same hair length at the end so we can set these two equations as equal to each other:

23 + 3x = 27 + 1x Subtract 23 from both sides

3x = 4 + 1x Subtract 1x from both sides

2x = 4 Divide by 2

x=2 Now we know it will take 2 months for their hair to be the same length!

Let's plug that in to our original equations:

Ann's hair length = 23 + 3(2) = 29 centimeters

Malia's hair = 27 + 1(2) = 29 centimeters

It will take 2 months for the girls to grow their hair to the same length of 29 centimeters.

As ordered pairs, with x as the number of months, we can use the length of the girls hair as the y value.

At 0 months, Ann's hair is 23 cm and Malia's is 27 cm so the first ordered pairs are (0, 23) and (0, 27).

At 1 month, Ann's hair grows 3 cm and Malia's grows 1 cm so the second pairs are (1, 26) and (1, 28).

Finally, at 2 months Ann's hair is at 29 cm and so is Malia's so the final ordered pair is (2, 29) for both girls.

If you were to draw these equations on a graph, (2, 29) is where the lines would intersect.