Question

(a)

Two friends, Jeanette and Zoe, 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. Jeanette's hair is already 29 centimeters long and grows at a constant rate of 1 centimeter per month. Zoe's hair is 12 centimeters and growing at a speed of 2 centimeters 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?





Part A:



Using the variables y for total growth and x for rate of change answer the questions below.



Create the equation for Jeanette's hair growth:


Create the equation for Zoe's hair growth

Answer 1

Explanation:

J: y = 29 cm + (1 cm/mo)x

Z: y = 12 cm + (2 cm/mo)x

29 cm + (1 cm/mo)x = 12 cm + (2 cm/mo)x

Solve for x to find how many months it will take for them to have the same length of hair:

29 cm - 12 cm = (2 cm/mo)x - (1 cm/mo)x

17 cm = (1 cm/mo)x

x = (17 cm) / (1 cm/mo) = 17 months

Plug this value for x (17 months) into the equations to find how long their hair will be:

J: y = 29 cm + (1 cm/mo)(17 mo) = 46 cm

Z: y = 12 cm + (2 cm/mo)(17 mo) = 46 cm

This shows that it will take 17 months for each girl's hair to be 46 cm long.