SOLUTION: tutors will you please help me with this problem I can't figure it out and this is my last one, Two years ago,Kelli was three times as old as Tif was then. In 5 years Ke

Question 30008: tutors will you please help me with this problem I can't figure it out and this is my last one,
Two years ago,Kelli was three times as old as Tif was then. In 5 years Kelli will be only twice as old as Tif. How old is each now?In 5 years? and 2 years ago?
Kelli now-
Tif now-
Kelli in 5 years-
Tif in 5 years-
Kelli 2 years ago?
Tif 2 years ago?
Found 2 solutions by josmiceli, Paul:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let K = Kelli 's age now
Let T = Tif's age now
Two years ago, Kelli's age = K-2
Two years ago, Tif's age = T-2
Five years from now, Kelli's age = K+5
Five years from now, Tif's age = T+5
[1] K - 2 = 3(T - 2)
[2] K + 5 = 2(T + 5)
There are two equations with two unknowns, so I can solve them
Subtract 7 from both sides of [2]
K + 5 - 7 = 2(T + 5) - 7
K - 2 = 2T + 10 - 7
K - 2 = 2T + 3
Subtract this equation from [1]
0 = 3(T - 2) - (2T + 3)
Add (2T + 3) to both sides
2T + 3 = 3(T - 2)
2T + 3 = 3T - 6
Subtrtact 2T from both sides
3 = T - 6
Add 6 to both sides
T = 9
Substitute this age for T in [1] or [2]
In [1]
K - 2 = 3(T - 2)
K - 2 = 3(9 - 2)
K = 21 + 2
K = 23
check these answers by substituting in [2]
K + 5 = 2(T + 5)
23 + 5 = 2(9 + 5)
28 = 2 * 14
28 = 28
it checks
Substitute in [1]
K - 2 = 3(T - 2)
23 -2 = 3(9 - 2)
21 = 3 * 7
21 = 21
checks
Tif's age now is 9
Kelli's age now is 23
Tif in 5 years
T + 5 = 14
Kelli in 5 years
K + 5 = 28
Tif 2 years ago
T - 2 = 7
Kelli two years ago
K -2 = 21
Answer by Paul(988) (Show Source): You can put this solution on YOUR website!
Kelli's age =x
Tif's age = y
Tif's age 2 years ago = y-2
Kelli's age 2 years ago = x-2
Five years from now:
y+5
and
x+5

Equations:

Solve for y in first:
y=3x-6+2
y=3x-4

Sub for y in second.
2x+10=3x-4+5
-x=-9
x=9

y=3(9)-4
y=23

Hence, Tif is 9 years old and Kelli is 23 years old.
Paul.

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