Question

Your friend is trying to grow her hair as long as her cousin's hair. The table (attached) shows their hair lengths (in inches) in different months.

a. Write a system of linear equations that represents this situation.
b. Will your friend's hair ever be as long as her cousin's? If so, in what month?

Answer 1

a) y = 1/2x + 5/2

y = 2/5x + 29/5

b) hair will be 19 inches for both at 33 months

Explanation:

a) rate of growth of friend's hair: (3, 4) (8, 6.5)

(6.5 - 4) ÷ (8 - 3) = 2.5/5 or 1/2

find the y-intercept of equation for growth of friend's hair:

y = mx + b

4 = 1/2(3) + b

4 = 3/2 + b

8/2 - 3/2 = b

5/2 = b

equation for growth of friend's hair:

y = 1/2x + 5/2

rate of growth of cousin's hair: (3, 7) (8, 9)

(9 - 7) ÷ (8 - 3) = 2/5

find the y-intercept of equation for growth of cousin's hair:

y = mx + b

9 = 2/5(8) + b

9 = 16/5 + b

45/5 - 16/5 = b

29/5 = b

equation for growth of cousin's hair:

y = 2/5x + 29/5

b) y = 1/2x + 5/2

y = 2/5x + 29/5

1/2x + 5/2 = 2/5x + 29/5

5/10x + 25/10 = 4/10x + 58/10

1/10x = 33/10

10x = 3300

x = 33