Robert is three times as old as Catherine now. In 8 years time, the ratio of their age will be 2:1. How old is Catherine now?

Question

Let x be Catherine's age now.
Y be Robert's age now.
My answer is in fractions, y =8/3 , it probably is wrong, some help please..

Answer 1

x = Catherine's age (now)

3x = Robert's age (now)

in eight years,

(x + 8) = Catherine's age
(3x + 8) = Robert's age

(3x + 8)/(x + 8) = 2/1

3x + 8 = 2x + 16
3x-2x+8=2x-2x+16
x+8=16
x+8-8=16-8
x = 8
Catherine is 8 years old after 8 years
Robert is 24 years old after 8 years

Answer 2

Thks for the answer but can you do one in two variables?

Answer 3

R = Roberts age

C = Catherine age

The ratio of their age now :

R / C = 3 Multiply both sides by C

R * C / C = 3 C

R = 3 C

The ratio of their age after 8 years :

( R + 8 ) / ( C + 8 ) = 2 / 1 = 2

( 3 C + 8 ) / ( C + 8 ) = 2 Multiply both sides by C + 8

( 3 C + 8 ) * ( C + 8 ) / ( C + 8 ) = 2 * ( C + 8 )

3 C + 8 = 2 C + 16 Subtact 2 C to both sides

3 C + 8 - 2 C = 2 C + 16 -2 C

C + 8 = 16 Subtract 8 to both sides

c + 8 - 8 = 16 - 8

C = 8 years

Proof :

C = Catherine age = 8 yr

R = Roberts age = 3 * 8 = 24 yr

After 8 years Catherini wil be 8 + 8 = 16 years old.

Robert will be 24 + 8 = 32 years old

32 / 16 = 2