How old is each now?

Question

Ten years ago Linda was three times Christy's age then. Ten years from Christy's ages will be 4/7 of Linda's age.

Answer 1

L - 10 = 3 * (C - 10)
C + 10 = (4/7) * (L + 10)

L - 10 = 3C - 30
L = 3C - 20

C + 10 = 4L/7 + 40/7
7C + 70 = 4L + 40
7C + 30 = 4L
7C + 30 = 4 * (3C - 20)
7C + 30 = 12C - 80
110 = 5C
C = 22

L - 10 = 3 * (C - 10)
L - 10 = 3 * (22 - 10)
L - 10 = 3 * 12
L - 10 = 36
L = 46

Answer 2

L = actual Linda's age
C = actual Christy's age
L - 10 = Linda's age ten years ago
C -10 = Christy's age ten years ago
L + 10 = Linda's age in ten year later
C + 10 = Christy's age in ten year later

Equations system to solve :

(1) L -10 = 3(C -10)
(2) C + 10 = 4div7(L+10)

(1) L - 10 = 3C - 30
(2) (4div7)L + 40div7 = C + 10

(1) L - 3C = -20
(2) 4div7 -C = ( -40div7) + 10

(1) L - 3C = -20
(2)' x3 ( -12div7) + 3C = (30div7) x(-3)
-------------------------------------------------------
(-5div7)L = (-140div7) (-90div7)

L = -230div7

L = (-230div7) x (-7div5)

L = 46


Substituted L = 46 in (1)

We have : 46 -10 = 3C - 30

3C -30 = 36

3C = 66

C = 22


Answer : C = Christy = 22 years old
L = Linda = 46 years old


Verification :

(1) 46 -10 = 3(22 -10)
36 = 3( 12)
36 = 36

(2) 22 + 10 = (4div7)(46 + 10)
32 = (4div7)(56)
32 = 4 x 8
32 = 32

Answer 3

Let the present age of Christy and Linda be
C and L years respectively
Ten years ago Christy's age was C-10 and that of Linda was L-10 years respectively and ten years from now Christ's and Linda's age will be C+10 and L+10 respectivly
Therefore according to the problem
L-10=3(C-10)
or L-10=3C-30
or,L-3C= -30+10= -20.....(eqn 1)
From the second condition,we get
C+10=4/7(L+10)
or,7c+70=4(L+10 [multiplying both sides by 7]
or,7C+70=4L+40
or,-4L+7C=40-70= -30.....(eqn. 2)
Multiplying eqn.(1)by 4 and adding it with eqn(2)
4L-12C= -80
-4L+7C=-30
(Adding) -5C= -110
Therefore C= -110/-5=22
Putting the value of C in eqn 1
L-3*22=-20
or,L-66= -20
L= -20+66=46
Therefore present age of Linda is 46 years and that of Christy is 22 years