a brother and sister split the $840,500 from the sale of their parents house. According to the will, the sister is supposed to get 5% more for managing the hou

Question

a brother and sister split the $840,500 from the sale of their parents house. According to the will, the sister is supposed to get 5% more for managing the house.  How much does she get?

 

The answer is 430,500

Answer 1

Melvyne,

I can see where this vague language might cause some confusion. One might easily assume that it meant the brother gets 47.5% and the sister gets 52.5%. But that is not the right answer. So they must mean that whatever the brother's share, 5% of that is how much more the sister gets. We set this up with a pair of equations.

 

B + S = 840,500    and      S = 1.05B

 

Since we want to find the sister's share, we want to rewrite the second equation in terms of S:

 

B = S/1.05

 

and now substitute into the first equation.

 

S/1.05 + S = 840,500

 

To get rid of the fraction, multiply the whole equation by 1.05

 

S + 1.05S = 882,525

 

Combine like terms.

 

2.05S = 882,525

 

Divide by 2.05

 

S = 882,525 / 2.05 = 430,500

 

I hope that cleared it up for you.

Answer 2

Let x = amount the brother gets

 

y = amount the sister gets

 

x + y = total sale = 840500

 

y = 5% more than x, so y = 1.05x, or we can say 1.05x - y = 0

 

Now we have two equations in two unknowns x and y:

 

x + y = 840500

1.05x - y = 0

 

Get y = 840500 - x from top equation and substitute into bottom equation to find x:

 

1.05x - (840500 - x) = 0

 

2.05x = 840500

 

x = 840500/2.05 = 410,000

 

y = 1.05x = 1.05(410.000) = 430500

 

He gets $410,000, she gets $430500.