Show a complete solution to each problem. Mary's assets....

Show a complete solution to each problem. Mary's assets. Mary Hall's will specifies that her lawyer is to liquidate her assets and divide the proceeds among her three sisters. Lena's share is to be one-half of Lisa's, and Lisa's share is to be one-half of Lauren's. If the lawyer has agreed to a fee that is equal to $10 \%$ of the largest share and the proceeds amount to $\$ 164,428,$ then how much does each person get?

Show a complete solution to each problem.
Mary's assets. Mary Hall's will specifies that her lawyer is to liquidate her assets and divide the proceeds among her three sisters. Lena's share is to be one-half of Lisa's, and Lisa's share is to be one-half of Lauren's. If the lawyer has agreed to a fee that is equal to $10 \%$ of the largest share and the proceeds amount to $\$ 164,428,$ then how much does each person get?

Key Concepts

Asset Division with Fees

This involves dividing a total amount among several parties according to specified criteria while accounting for additional deductions like fees. The concept requires combining the ratios of the distribution with the subtracted percentage fee to form a complete solution that ensures the sum of the parts matches the overall total.

Percentage Calculation

Understanding how to compute percentages is key when additional fees are based on a portion of a particular share. This concept allows one to calculate a specific percentage of a quantity (such as a fee being a percentage of the largest share) and then incorporate that into the overall distribution.

Algebraic Equations

Algebraic equations are used to model relationships between quantities described in the problem. By assigning variables to unknown amounts and setting up equations based on the given ratios and total sum, one can systematically solve for the individual amounts.

Ratios and Proportions

This concept involves interpreting the relationships between different quantities using relative sizes. In problems like this, ratios describe how one share compares to another, allowing the conversion of proportional relationships into mathematical expressions that help solve for unknown values.

Transcript

00:01 Okay, in this problem, we're asked to show a complete solution for the following.

00:05 So there are assets being divided between three people.

00:08 Person a is to get one half of what person b gets.

00:12 Person b is to get one half of what person c gets.

00:16 And there's also a lawyer that needs to be paid a fee that is going to be 10 % of the largest share.

00:24 So whatever the largest amount paid out to one of those three people, they get 10 % of that.

00:30 So the total assets are equal to $164 ,428.

00:40 And we want to know how much does each person get? so you can see off to the left and blue, i've made a list of people we need to account for a win.

00:48 So we need to account for person a, b, c, and the lawyer represented by l.

00:53 So, in short, persons a inheritance plus person b's inheritance plus person c's inheritance, plus the cost of the lawyer are all going to add up to $164 ,428.

01:14 So we need to figure out how to write this out in an equation with a single variable.

01:19 So looking at our problem, i can tell that person c is going to have the largest amount given to them.

01:29 And i can tell that because person a is going to get one half of what person b gets, and person b gets one half of what person c gets.

01:36 So they get the largest inheritance.

01:38 Everything is going to be based off of person c.

01:41 So i'm going to use c as my variable in this problem.

01:46 So i'm going to go ahead and start my problem.

01:49 Right here then underneath c we're just going to use c to represent that well i know that's the lawyer costs are going to be 10 % of the largest share which is c in this case so 0 .1 of c or 0 .10 of c that's going to be the lawyer costs so let's look at person b person b is to get one half of person c's inheritance so one half of c and then for the last person b person accounted for.

02:21 Person a gets one half of what person b gets.

02:25 So i can take one half of person b's inheritance of one half of c.

02:33 Okay.

02:34 And all of that equals $164 ,428.

02:39 So we got quite a lengthy equation here.

02:43 So let's go ahead and start simplifying some of these things.

02:47 So first of all, i'm going to take my one -half, multiplied by one half c and figure that out so i'm going to go ahead and change this to a decimal so 0 .5 multiplied by 0 .5 same means one half times one half c equals 0 .25 or 1 4th c okay so 0 .25c let's in fact change these all to decimals so 0 .25c plus 0 .25c plus 0 .5c plus 0 .1c equals 0 .1c equals $164 ,428.

03:25 So now i can go ahead and combine all of my like terms...

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