Question 272068: 1. Four years ago, Katie was twice as old as Anne was then. In 6 years, Anne will be the same age that Katie is now. How old is each now?
2. Adam is 5 years younger than Eve. In one year, Eve will be 3 times as old as Adam was 4 years ago. Find their ages now.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 1. Four years ago, Katie was twice as old as Anne was then.
k - 4 = 2(a - 4)
k - 4 = 2a - 8
k = 2a - 8 + 4
k = 2a - 4
In 6 years, Anne will be the same age that Katie is now. How old is each now?
a + 6 = k
Substitute for k in the equation: k = 2a - 4, find a
a + 6 = 2a - 4
6 + 4 = 2a - a
a = 10 yrs is A's present age
and
k = 2(10) - 4
k = 16 hrs is K's present age
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2. Adam is 5 years younger than Eve.
a = e - 5
In one year, Eve will be 3 times as old as Adam was 4 years ago.
e + 1 = 3(a - 4)
e + 1 = 3a - 12
e = 3a - 12 - 1
e = 3a - 13
replace a with (e-5), find e
e = 3(e-5) - 13
e = 3e - 15 - 13
e = 3e - 28
28 = 3e - 3
2e = 28
e = 14 yrs is E's age
and
a = 14 - 5
a = 9 yrs is A's age
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