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My age is one-half of my mother`s age plus 3.In 2 years my age plus 20 will be the same as my mother`s age 6 years ago.If my mother is 4 years younger than my father,how old will i be next year? show me the solution

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X= (1/2)M + 3 2 + X + 20 = M - 6
The father statement is not needed.
Two variables, with two equations. Solve for X.

Posted on Sep 29, 2010

  • 1 more comment 
  • CameraR
    CameraR Sep 29, 2010

    Oh, remember to add 1 to the answer, as the question asks how old will I be next year.

  • CameraR
    CameraR Sep 29, 2010

    For some reason the original equation meshed together. Two independent equations as follows:

    X= (1/2)M 3

    2 X 20 = M - 6

  • CameraR
    CameraR Sep 29, 2010

    For some reason the original equation meshed together. Two independent equations as follows:

    X= (1/2)M 3

    there's a break here

    2 X 20 = M - 6



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Adjoa is three years older than her brother years ago,the sum of their ages 13years.calculate the sum of their present ages.

Let Adjoa's age be x and Kwame's y.
  • Adjoa is 3 years older than Kwame: x=y+3
  • Seven years ago sum of their ages was 13: (x-7)+(y-7)=13
  • Now you substitute first equation into second equation: (y+3-7)+(y-7)=13
  • 2y-4-7=13
  • 2y=24
  • y=24/2=12 years
  • x=y+3=12+3=15 years
  • sum of their present ages is x+y=12+15=27 years

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"quadratic function" diophantus , a greek

Let x be Diophantus' age when he died.

His son died 4 years before Diophantus (so Diophantus was then x-4 years old). His son lived half as long as Diophantus so when he (son) died he was x/2.
Diophantus' son was born when Diophantus was (x-4)-x/2 years old. That was 5 years after his marriage so when Diophantus married he was (x-4)-x/2-5 years old. We also know that 1/6 of his life was spent in childhood, 1/12 in youth and 1/7 as bachelor so (x-4)-x/2-5=(1/6+1/12+1/7)x.
Now you solve last equation:
  • x-4-x/2-5=11/28x
  • x/2-11/28x=4+5
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Diophantus was 84 years old when he died.

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The sum of ages of marian, diana and carlos are 17. Two years from now marian will twice as old as diana. if carlos is half as old as marian four years from now. How ald are they now ? Pls show the...

Let m be Marian's age, d Diana's age and c Carlos age.
  • sum of ages is 17: m+d+c=17
  • two years from now Marian will be twice as old as Diana: m+2=2*(d+2) so m+2=2d+4 so 2d=m-2 or d=(m-2)/2=m/2-1
  • Carlos will be half as old as Marian 4 years from now: c+4=1/2(m+4) or c+4=m/2+2 or c=m/2-2
  • now: m+d+c=m+m/2-1+m/2-2=17
  • 2m=17+3=20
  • m=20/2=10 years
  • d=m/2-1=5-1=4 years
  • c=m/2-2=5-2=3 years
Marian is 10 years old, Diana 4 years old and Carlos is 3 years old.

I hope I helped :)

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Cory is 6 years older than her sister.Four years ago, she was 4 times as old her old is cory now?

let c = cory's age now let s = her sisters age now
cory's age now = sisters age + 6 years
=> c = s + 6
4 years ago, cory was 4 years younger ( i.e. c-4) and her sister was 4 years younger (s- 4)
4 years ago cory was 4 times older than her sister
=> c - 4 = 4*(s-4)
We can simplify this to c = 4s - 16 +4 c = 4s - 12
We can then use simultaneous equations to solve the two equations
(i) c = s + 6 (ii) c = 4s - 12
If we multiply both sides of equation (i) by 4 we get (iii) 4c = 4s + 24
We can then subtract equation (ii) from equation (iii) to eliminate the '4s' term => ( 4c = 4s + 24 ) - (c = 4s - 12) => 4c - c = 4s +24 - 4s +12 => 3c = 4s - 4s +36 => 3c = 36 => c = 36/3 => c = 12 => Cory's age now = 12
For clarity: Her sister's age now is of course 6 4 years ago Cory would of been 8 and her sister would of been 2
I hope this helps and good luck! If you have more questions - ask away!
Please take the time to rate this answer
Many Thanks Don.

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Bob was thrice as old as peter. Six years ago he was 4 times as old as peter . Find their ages now?

Correction: Bob is thrice as old as Peter.
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Six years earlier the relations was: b-6=4*(p-6)=4p-24.
Take the 6 to the right side leaving b=4p-18
Remember that now b=3p. Use it in the equation above
b=(3p)=4p-18, This becomes 3p=4p-18 or 0=p-18, and p=18
Peter is 18 years old, and Bob is 3*18=54 years old.
Verification: 6 years ago Peter was 12 years old and Bob 48 years old. 48/12=4.

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Four years ago allan was three less than twice roys age in 5years allan will be 6yeras older than roy how old are they?

Allan is 19 and Roy is 13.


First we have 2 variables, their ages: I used Allan = x & Roy = y
Equation 1: X - 4 = 2*(Y-4) - 3
We can ignore the 5 years in the second part of the statement. Allan will always be 6 years older than Roy whether it be 5 years from now or ten years form now.
Equation 2: X = Y + 6

Substitute Y + 6 for X in equation 1:
X - 4 = 2*(Y-4) - 3 becomes Y + 6 - 4 = 2*(Y-4) - 3
That simplifies to Y + 2 = 2Y - 8 - 3
Rewrite it again: Y + 2 = 2Y - 11
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