Question

Write a system of equations to describe the situation below, solve by using substitution, and fill in the blanks Two friends,Rita and Mariana,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,Rita's hair is already 18 centimeters long and grows at a constant rate of 2 centimeters per month. Mariana hair is 12 centimeters and growing at a speed of 3 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 that take? How long will their hair be?

Answer 1

Rita = r = 18 cm speed = 2 cm/m

Mariana = m = 12 cm speed = 3 cm/m

Equations

18 + 2l = 0

12 + 3l = 0

System of equation

18 + 2l = 12 + 3l

18 - 12 = 3l - 2l

6 = l

Time = 6 months

Length Rita's hair length = 18 + 2(6)

= 18 + 12

= 30 cm

Mariana's hair length = 12 + 3(6)

= 12 + 18

= 30 cm

Conclusion: It will take 6 months to Mariana and Rita to have the same length of their hair, it will be 30 cm.