Rosa is 14 years older than her sister amy. Three years ago, she was three times as old as amy. how old is each girl now?
R = Age of Rosa
A = Age of Amy
Rosa is 14 years older than her sister Amy.
R = A + 14
Three years ago, she was three times as old as amy
Three years ago, Rosa and Amy was 3 years younger so.
R - 3 = 3 ( A - 3 )
Replace R with A + 14
A + 14 - 3 = 3 ( A - 3 )
A + 11 = 3 A - 3 * 3
A + 11 = 3 A - 9 Add 9 to both sides
A + 11 + 9 = 3 A - 9 + 9
A + 20 = 3 A Subtract A to both sides
A + 20 - A = 3 A - A
20 = 2 A Divide both sides by 2
20 / 2 = 2 A / 2
10 = A
A = 10
R = A + 14
R = 10 + 14
R = 24
Rosa is 24 year old
Amy is 10 year old
ages now:
Amy --- x
Rosa --- x+14
Three years ago:
Amy --- x-3
rosa ---- x+11
x+11 = 3(x-3)
x+11 = 3x - 9
2x = 20
x = 10
sub into my definitions
three times Rosa’s age in 5 years if she is x years old today
To determine the ages of Rosa and Amy now, we can use a system of equations.
Let's assume Amy's current age is x years.
Therefore, Rosa's current age would be x + 14 years (since Rosa is 14 years older than Amy).
Three years ago, Amy's age would have been x - 3 years, and Rosa's age would have been (x + 14) - 3 years = x + 11 years.
According to the given information, three years ago Rosa's age was three times Amy's age. So we can write the equation:
x + 11 = 3(x - 3)
Now we can solve this equation to find the value of x.
x + 11 = 3x - 9 (Multiplying 3 with x and -3)
2x = 20 (Adding 9 to both sides and simplifying)
x = 10 (Dividing both sides by 2)
Therefore, Amy's current age is 10 years.
Substituting this value back into our earlier assumption, we can find Rosa's current age:
Rosa's current age = Amy's current age + 14
Rosa's current age = 10 + 14 = 24 years
So, Rosa is currently 24 years old, and Amy is currently 10 years old.