a mon wants to do something

Question

A mother plans to have 4 children and distribute her estate, worth $400000 between them as follows: ¼ of the estate is to be split equally among the children. For the rest, each child is to receive $3000 every year until all the money is given out. As soon as the first child is born she puts his\her money in one account. When the second child is born she puts also his\her part in another account, and so on. Given that the children are all 4 years apart, how much would each receive from their mother’s estate?

(Hint: Let “x”, “y”, “z” and “w” be the amount of money that each child will receive from the splitting of of the estate according to age, starting with the oldest one.)

Answer 1

As ¼ of the estate is to be split equally among the 4 children i.e. ¼ of the $400000 = $100000 is distributed equally between the 4 children which is  $25000 (¼ of 100000 ) and remaining amount i.e. $400000-$100000=$ 300000 distributed according to their ages $3000 every year until all the money is given out . Since  the children are all 4 years apart let their ages will be like a, a+4, a+8 and  a+12 years

 

 

So, first child will  get  amount (x)  = 25000 +a*3000

    second child will get amount (y)  = 25000 + (a+4)*3000

    third child will get amount    (z)  = 25000 + (a+8)*3000

    fourth child will get amount   (W) = 25000 + (a+12)*3000

 

And sum of each child share will be equal to $400000

i.e

                                           

 

 

     x  +   y  +  z  +   w   =    $400000

25000 +a*3000 +25000 + (a+4)*3000+ 25000 + (a+8)*3000 + 25000 + (a+12)*3000= 4000000

         100000+a*3000 +a*3000+ 4*3000+a*3000+8*3000+a*3000+12*3000    =400000

         100000+ 3000a+3000a+12000+3000a+24000+3000a+36000= 400000

                                                          172000+ 12000a        =  400000

                                                                        12000a         =400000-172000

                                                                        12000a         = 228000

                                                                                  a = 228000/12000

                                                                                 a  = 19

Now put the value of and find out values of x,y,z and w