Mr. Evans' will states that each of his children will receive an equal

Question

Mr. Evans' will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 5 children and 6 grandchildren, then approximately what percentage of Mr. Evans' estate will each grandchild receive?

A. 20%
B. 17%
C. 4.0%
D. 3.3%
E. 2.8%

A. 20%
B. 17%
C. 4.0%
D. 3.3%
E. 2.8%

generis · Answer

This question's wording can be very tricky.

1) we need  at least  5 shares

-- Mr. E has five children, and "each of his children will receive an equal share of his estate..."
--That means: each one of 5 children gets an equal share
--It does NOT mean: the estate is divided into 5 parts (that leads to trap answer D)

2) We need more than 5 shares. The set of grandchildren is like a sixth child. 
-- Mr. E's grandchildren "  split  a  portion   . . . equal to  the share  received by  each  of his children."
-- That means: his grandchildren,  as a set , also get one share equal to that of one child
-- It does NOT mean: the estate is divided into 5 equal parts, AND THEN 6 grandchildren share  \frac{1}{5}

Where is the other  \frac{1}{5}  coming from  if the estate has been divided already?
Will one of the children hand over his or her fifth to the grandchildren? NO

3) We must divide the estate into SIX equal portions**
 
• 5 children each get 1 portion;  \frac{5}{6}  of total estate
• One  set  of grandchildren receives 1 portion,  \frac{1}{6}  of total estate

4) What  portion  does each (one) grandchild get?
• One  set  of 6 grandchildren gets  \frac{1}{6}  portion 
• Each grandchild's portion is  \frac{\frac{1}{6}}{6} = \frac{1}{36}

5) What  percentage  of Mr. Evans's estate does each (one) grandchild receive?
• A portion is a part of a whole
• Percentage:   \frac{Part}{Whole} * 100

\frac{1}{36}*100\approx{.0277}*100\approx{2.8}  percent

Answer E

**
Let X = a portion, C = one child, G = the  set  of grandchildren

The estate gets divided this way:
X |X |X |X |X |X
C |C |C |C|C |G

Once you realize you need 6 portions, if the fractions aren't clear, you can assign values

Let the estate be worth $72
X =  \frac{$72}{6}  = $12
The set of grandchildren receives X = $12
There are 6 grandchildren
Each grandchild receives  \frac{$12}{6}  = $2

What percentage of the estate does each grandchild receive?
Percentage:  \frac{Part}{Whole} * 100 
 \frac{2}{72} * 100 = \frac{1}{36} * 100\approx{.0277}*100 \approx{2.8}  percent

omavsp · Answer

He has 5 children and 6 grandchildren that will split as if they were one child of his.

so in total - 6 children, one of which will split by another 6.

I took the number 360 (multiple of 6 and 6).

each child will receive 60, and each grandchild will receive 10.

(10/360)*100 = less than 3 percent but close -  2.8 is our answer .

PRI23YA · Answer

Let the estate be 120 units. Each child receives equal parts and the same each equal part is received by 6 grand children as well.

Therefore, 120 is divided here into 6 parts for 20 units each. 
Each child gets 20; each grandchild gets 20/6 units.

Now each grandchild's share= (20/6)/120 *100= 2.77~2.8%

Regor60 · Answer

Each child will get an equal portion of the estate.

Call this portion:

1/X

Total amount allocated to 5 children:

5*1/X = 5/X

Each of the 6 grandchildren will receive an equal portion of the amount allocated to each child:

(1/X)/6 = 1/(6X)

Total amount allocated among 6 grandchildren:

6*1/(6X) = 1/X

The amounts allocated to the children and grandchildren must total 1:

5/X + 1/X = 6/X = 1, therefore:

X = 6

Since each grandchild will receive 1/(6X), their portions are:

1/(6*6) = 1/36 = 3/108 =

slightly less than 3%

Posted from my mobile device

luisdicampo · Answer

Deconstructing the Question

Mr. Evans has  5 children . 
Each child receives an equal share of the estate. 
The  6 grandchildren  together receive a portion equal to the share of one child.

Step-by-step

Let total estate be  E .

Children receive:

5 	ext{ equal shares}

Grandchildren together receive:

1 	ext{ share}

So the estate is divided into:

6 	ext{ equal shares}

Each child receives:

\frac{E}{6}

Grandchildren together receive:

\frac{E}{6}

Each grandchild receives:

\frac{E}{6} \div 6 = \frac{E}{36}

Fraction of estate:

\frac{1}{36} \approx 0.0278

Convert to percent:

\approx 2.8\%

Answer: 2.8%

Mr. Evans' will states that each of his children will receive an equal

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Mr. Evans' will states that each of his children will receive an equal

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615 to 715 in 15 Days (Ria's Strategies)

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