Equation word problem

Question

Scott is four times older then Beth. In six years from now Scott will only be three times older then Beth. Write down equations to describe the relationship between their ages. Now solve the equations to find out how old each of them is now. Please show all working. Thank you. 

Answer 1

y= Scott's age

x= Beth's age

 

y = 4x

y + 6= 3 (x+6)

 

Substitute first equation into second equation to get:

4x + 6= 3 (x+6)

4x + 6= 3x +18

x = 12

 

Now Scott is 48 and Beth is 12, In 6 years Scott is 54 and beth is 18.

Answer 2

let y be age of scott and x be age of Beth

y =4x   -------- Scott is 4 times older then Beth------equation 1

y+6=3(x+6) ----- in 6 years Scott will be 3 times older then Beth-----equation 2

 

Substitute y=4x in equation 2

4x+6 =3x+18

x=12  - Beth Present age

y=4x = 4*12 =48 - Scott Present age

 

Therefore Beth is 12 years ole

Scott is 48 years old