Rosa is 14 years older than her sister Amy. 3 years ago, she was 3 times as old as Amy. How old are they now?
R=age of Rosa
A=age of Amy
then form two equations using information given:
"Rosa is 14 years older than her sister Amy." =>
R-A=14 =>
R=A+14.................(1)
"3 years ago, she was 3 times as old as Amy."
Three years ago, both were 3 years younger, so
(R-3)=3*(A-3)
Simplify:
R=3A-9+3 =>
R=3A-6................(2)
Solve for R and A using equations (1) and (2).
Hint: use substitution to solve for R and A.
To solve this problem, let's define the variables:
Let x be Amy's age now.
Rosa's age can be expressed as: x + 14 (since Rosa is 14 years older than Amy).
Three years ago, Amy's age was x - 3, and Rosa's age was (x + 14) - 3 = x + 11.
According to the problem, three years ago Rosa was three times as old as Amy, so we can set up the equation:
x + 11 = 3(x - 3)
Now, let's solve the equation:
x + 11 = 3x - 9
11 + 9 = 3x - x
20 = 2x
x = 10
So Amy's current age (x) is 10 years old.
Rosa's current age is x + 14 = 10 + 14 = 24 years old.
Therefore, Amy is currently 10 years old, and Rosa is currently 24 years old.