Today my age is 1/3 Mother's age plus 1/10 Father's. I am exactly two decades old. How old are Mother and Father?

Question

Today my age is 1/3 Mother's age plus 1/10 Father's.  It is also true that today my age is 2/9 Mother's plus 1/5 Father's. I am exactly two decades old.  How old are Mother and Father?

 

This is from College Algebra Chapter 2

 

Answer 1

Hello Rod,

This is a long problem, so I will try to be as thorough as I possibly can. 

First, I am going to identify what the variables represent. Then, I am going to set up two equations. Next, I am going to use the Elimination Method to isolate one of the variables, in this case it will be f. After I find the value of f, I will plug its value into one of the equations to find the value of m.  By the way the father is 50 and the mother is 45,

 

a) Let f be the age of the father

b) Let m be the age of the mother

c) The problem states that you are two decades old, so you are 20,

 

Now, let's set up the equations

my age is 1/3 my mother's age plus 1/10 my father's age is translated as follows, remember you are 20!

 

1) 20= 1/3 m + 1/10 f

 

Next, it is also true that I am 2/9 my mother's age plus 1/5 my father's age can be translated as 

 

2) 20= 2/9 m+ 1/5 f

 

What I am going to do next is to clear the fractions.  So, I am going to multiply equation #1 from above by 30 and equation # 2 by 45. 30 and 45 are the least common denominator for equations #1 and #2, respectively. 

 

Here we go, 

 

30 [ 20= 1/3 m + 1/10 f]=

     600= 30/3 m + 30/ 10 f     I used the distributive property

     600= 10m      + 3 f            I just simplified the fractions

Next

45 [ 20= 2/9 m + 1/5 f ]

      900= 90/9 m + 45/5 f        Again, I used the distributive property

       900= 10m + 9 f                Simplifying the fractions

So, we have

 

1) 600= 10m+ 3f

2) 900= 10m + 9f

 

I am going to isolate the variable f by multiplying equation #1 by -1, so equation #1 becomes

 

1) -600= -10m - 3f

2)  900=   10m + 9f

3)  300=    0m  + 6f       I added equations #1 and #2 to get # 3

        50 = f                    I divided both sides by 6

 

So, the father is 50.  To find the mother's age, I will substitute 50 for f into one of the two original equations.  I am going to use

 

20= 1/3 m + 1/10 f

20= 1/3 m+ 50(1/10)        I substituted 50 for f

20= 1/3 m + 50/ 10

20=. 1/3 m + 5.                 I simplified the second fraction

-5                -5                   I am subtracting 5 from both sides

 

15=   1/3 m

3* 15 = 3 (1/3 m)               Multiplying by 3 so I get 1 m

   45   = m

So, the mother is 45 and the father is 50.

Finally, I thought I would never end typing.  

 

Hope this helps and make sure you practice before a test on this.

 

D.Y. Taylor

dont forget to rate me :)