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?
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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
