SOLUTION: One year from today, Amy will be two-thirds as old as Ann. Five years from today; Amy will be four-fifths as old as Ann. How old is Amy today?

Question 318498: One year from today, Amy will be two-thirds as old as Ann. Five years from today; Amy will be four-fifths as old as Ann. How old is Amy today?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Let Ann's age be x now.
Amy's age be y
..
after one year
ann - x+1
Amy y+1
(y+1)= 2/3 (x+1)
3(y+1)=2(x+1)
3y+3=2x+2
1. 3y-2x=-1
..
After 5 years
Ann x+y
Amy y+5
..
y+5 = 4/5 (x+5)
5(y+5)=4(x+5)
5y+25=4x+20
2. 5y-4x=-5
Multiply eq1 by 2 and subtract eq2
6y-4x-5y+4x=-2+5
y=3 Ann's age now
plug the value of y in eq1
3y-2x=-1
9-2x=-1
10=2x
x=5 Amy's age now
RELATED QUESTIONS
Ann and Bill are both celebrating their birthday today. Two years from now Ann will be... (answered by duckness73)

Amy was born when Phil was 24 years old. When Amy is 3 times as old as she is today,... (answered by josmiceli)

Amy was born when Phil was 24 years old. When Amy is 3 times as old as she is today,... (answered by ikleyn,MathTherapy)

Ann and Bill are both celebrating their birthday today. Two years from now Ann will be... (answered by ewatrrr)

Ann is 11 years old. Her aunt, Kate, turned 47 today. After how many years will Kate be (answered by ikleyn)

Ann is 11 years ago. Her Aunt, Kate turned 47 today. After how many years will Kate be as (answered by ikleyn)

Ann is 11 years .Her Aunt, Kate turned 47 today. After how many years will Kate be 3... (answered by josgarithmetic,ikleyn)

Ann is 11 years ago. Her Aunt, Kate turned 47 today. After how many years will Kate be as (answered by josgarithmetic,ikleyn)

anns age is three times kims in four years from now ann will be twice as old as kim how... (answered by Maths68)