Mike is 30 years younger than his mother. In 5 years, Mike’s age will be ⅓ of his mother’s age.

Question

  Find Mike’s current age.

Answer 1

Let S = Mike's current Age

Let M = Mike's mom current age

 

Given: S = M - 30; S + 5 = ¹/₃ (M + 5)

S = M - 30 --> M = S + 30

 

Substitute M in the second given equation with "S + 30"

S + 5 = ¹/₃ (S + 30 + 5)

S + 5 = ¹/₃ (S + 35)

3S + 15 = S + 35

2S = 20

S = 10

 

Mike is 10 years old

 

Answer 2

x = mike's age, y= mom's age

 

1) Given information.

 

x + 30 = y

(x+5) = (y+5)/3

 

2) Rearrange 2nd equation for y.

 

3(x+5) = y+5

3x + 15 = y + 5

3x + 10 =y

 

3) Set the 2 equation equal and solve for x.

 

x+ 30 = 3x + 10

20 = 2x

10 = x

 

4) Solve for y.

 

y = 3(10) + 10

y=40