SOLUTION: Ten years ago Linda was three times christys age then. Ten years from now christys age will be 4/7 of Linda’s age then. How old are they now.

Question 1202331: Ten years ago Linda was three times christys age then. Ten years from now christys age will be 4/7 of Linda’s age then. How old are they now.
Found 4 solutions by mananth, ikleyn, Edwin McCravy, MathTherapy:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
Ten years ago Linda was three times christys age then. Ten years from now christys age will be 4/7 of Linda’s age then. How old are they now.
let christy's age 10 years ago be x
Linda's age was 3x
Ten years hence
Christy will be x+20 years
Linda'sage will be 3x +20
x+20 = 4/7 *3x
7(x+20) = 12x
7x+140 = 12x
5x = 140
x = 28 ( christy's age 10 years ago)
So Christy is 28 + 10 = 38 years
Plug x=28
Linda is 3x+10 = 84+20 =94 years

Answer by ikleyn(52799)   (Show Source): You can put this solution on YOUR website!
.
Ten years ago Linda was three times Christy's age then. Ten years from now
Christy's age will be 4/7 of Linda’s age then. How old are they now.
~~~~~~~~~~~~~~~~~~~~

            I read, interpret and solve the problem in different way;
            so my numbers are different from that of @mananth.

Let x years be the Christy's age 10 years ago; then Linda's age at that time was 3x years. Ten years from now Christy's age will be (x+20) years; Linda's age will be (3x+20) years then. So, I write equation as the problem states x + 20 = . Simplify and find x 7x + 140 = 12x + 80 140 - 80 = 12x - 7x 60 = 5x x = 60/5 = 12. ANSWER. Christy's age now is 12+10 = 22 years. Linda's age now is 3*12+10 = 46 years. CHECK. You may check it on your own that the condition of the problem "in ten years" is satisfied.

Solved.

Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!

I would set it up this way. This translates it literally just as it's stated. The answer comes out same as Ikleyn's. L = 46, C = 22 Edwin

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Ten years ago Linda was three times christys age then. Ten years from now christys age will be 4/7 of Linda’s age then. How old are they now. This is as clear as "daylight," so I don't know how 1 of these people didn't get it. It's not surprising though, considering the vast number of wrong answers he/she has been known to produce. Let Christy's and Linda's ages, be C and L, respectively Then 10 years ago, Christy was C - 10, while Linda was L - 10 We then get their AGE equation, 10 years ago as L - 10 = 3(C - 10)____L - 10 = 3C - 30___L = 3C - 20 ----- eq (i) In 10 years' time, Christy will be C + 10, while Linda will be L + 10 We then get their AGE equation, 10 years from now, as 7C + 70 = 4(L + 10) ------ Multiplying by LCD, 7 7C + 70 = 4L + 40 7C - 4L = - 30 ------ eq (ii) 7C - 4(3C - 20) = - 30 ----- Substituting 3C - 20 for L in eq (ii) 7C - 12C + 80 = - 30 - 5C = - 110' Christy's age, or Knowing Christy's age, you can now find Linda's age using eq (i)!

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