SOLUTION: May you pls help me with this question "In 9 years time,the mother will be twice as old as her son,she was 4 times older than her son after 3 years.find their age? Thank you tuto

Question 630202: May you pls help me with this question
"In 9 years time,the mother will be twice as old as her son,she was 4 times older than her son after 3 years.find their age?
Thank you tutor.
kaaliendjala@gmail.com
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if i interpret the question correctly, it looks like we have a very young mother.
the answer, as far as i can tell, is the age of the mother today is 9 years old and the son was just born so the age of the son is 0 years old.
in 9 years, the mother will be 18 and the son will be 9.
this means the mother is twice as old as the son.
in 3 years, the mother will be 12 and the son will be 3.
this means the mother is 4 times as old as the son.
unless i misunderstood the problem, this is the answer i get.
the problem as far as i can see is this.
statement 1:
In 9 years time,the mother will be twice as old as her son.
if we allow m to represent her age now, and s to represent her son's age now, then the equation we get from this statement is this:

m+9 = 2*(s+9)

statement 2:
she was 4 times older than her son after 3 years.

i interpreted this to mean that she was 4 times as old as her son in 3 years.
the equation for this would be:

m+4 = 4*(s+3)

if the interpretations are correct, then the mathematics works out as follows:

you have 2 equations that need to be solved simultaneously.
they are:

m+9 = 2*(s+9)
m+3 = 4*(s+3)

simplify these equations to get:

m+9 = 2*s+18
m+3 = 4*s+12

there are several ways to solve this, but the answer becomes s = 0 and m = 9
to confirm that this is the correct answer, solve both equations by substituting 0 for s and 9 for m.

the first equation of:
m+9 = 2*s+18 becomes:
9+9 = 2*0+18 which becomes:
18 = 18 which confirms that m = 9 and s = 0 works for the first equation.

the second equation of:
m+3 = 4*s+12 becomes:
9+3 4*0+12 which becomes:
12 = 12 which confirms that m = 9 and s = 0 works for the second equation.

since m = 9 and s = 0 works for both equations, that is the common solution to both equations.

it might look strange (a 9 year old mother would be very rare), but the mathematics comes out, assuming the interpretation of the problem is correct.

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