SOLUTION: At present Mary is 6 times as old as her daughter Susan. Four years from now she will be only four times as old as Susan. What is the sum of their ages at present?

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Question 1206436: At present Mary is 6 times as old as her daughter Susan. Four years from now she will be only four times as old as Susan. What is the sum of their ages at present?
Found 3 solutions by ikleyn, math_tutor2020, MathTherapy:
Answer by ikleyn(52796)   (Show Source): You can put this solution on YOUR website!
.
At present Mary is 6 times as old as her daughter Susan.
Four years from now she will be only four times as old as Susan.
What is the sum of their ages at present?
~~~~~~~~~~~~~~~~~~~~~~ 

Let x be the Susan current age, in years;
then the Mary's present age is 6x years, according to the problem.


Then in 4 years their ages will be (x+4) years for Susan and 6x+4 years for Mary.


So, we write an equation as the problem states

    4*(x+4) = 6x+4.


To solve it, simplify step by step

    4x + 16 = 6x + 4

    16 - 4 = 6x - 4x

       12  =    2x

        x  =   12/2 = 6.


Thus, the Susan's age is 6 years; the Mary's age is 6*6 = 36 years.


The sum of their ages at present is 6+36 = 42 years.    ANSWER

Solved.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

s = susan's current age
6s = mother's current age

Fast-forward 4 years into the future
s+4 = susan's future age
6s+4 = mother's future age

By this point the mother would be 4 times as old as Susan.
mother's future age = 4*(susan's future age)
6s+4 = 4*(s+4)
6s+4 = 4s+16
6s-4s = 16-4
2s = 12
s = 12/2
s = 6 is the daugther's current age
And,
6s = 6*6 = 36 is the mother's current age
Their current ages add to
6+36 = 42

Their future ages in 4 years would be:
susan = 6+4 = 10
mother = 36+4 = 40
The jump from susan's age to the mother is "times 4" since 10*4 = 40, which confirms we found the correct ages.


Answer: 42
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
At present Mary is 6 times as old as her daughter Susan. Four years from now she will be only four times as old as Susan. What is the sum of their ages at present?

Let Susan's age be S
Then mother's (Mary's) age is 6S
Sum of their ages: S + 6S = 7S

Four (4) years from now, Mary will be 6S + 4, and Susan will be S + 4
      We then get: 6S + 4 = 4(S + 4)
                   6S + 4 = 4S + 16
                  6S - 4S = 16 - 4
                       2S = 12
       Susan's age, or 
Sum of their ages: 7S = 7(6) = 42
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