linear equation

Question

a teacher is four times as old as a student. In 32 years, the students age will be half of the teachers age. How old are they now?

 

the age of the teacher =

The age of the student=

Answer 1

Let t = teacher's age and let s = student's age. Set up a system of equations:

 

t = 4s        (teacher is 4 times as old as student)

1/2(t + 32) = s + 32        (in 32 years, the student's new age will be half the teacher's new age)

 

 

Plug t = 4s into the second equation and solve for s:

 

1/2(4s + 32) = s + 32

2s + 16 = s + 32

s + 16 = 32

s = 16

 

 

The student is s = 16 years old, and the teacher is t = 4s = 4(16) = 64 years old.