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?
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..
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
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
Thks for the answer but can you do one in two variables?
To solve this problem, let's break it down into steps.
Step 1: Set up an equation using the given information.
Robert is three times as old as Catherine now. This can be expressed as:
Y = 3x
where Y is Robert's current age and x is Catherine's current age.
Step 2: Use the given information about the ratio in 8 years to set up another equation.
In 8 years' time, the ratio of their ages will be 2:1. This can be expressed as:
(Y + 8) / (x + 8) = 2 / 1
Step 3: Simplify the equation from step 2.
(Y + 8) / (x + 8) = 2
2(x + 8) = Y + 8
2x + 16 = Y + 8
Y = 2x + 8
Step 4: Substitute the equation from step 1 into the equation from step 3 and solve for x.
3x = 2x + 8
x = 8
Therefore, Catherine is currently 8 years old.