Algebra two help? anything is appreciated. (:?

Question

Old Mrs. Moore was having a party to celebrate her 90th birthday and needed to hire a reception hall in order to accommodate all her descendants. She invited her children and their spouses, her grandchildren and their spouses and all her great-grandchildren.

She has three times as many grandchildren as she had children and three times as many great-grandchildren as grandchildren. 86 people in all attended the party.

How many children did Mrs. Moore have?

Answer 1

There is nothing here that tells me anything about how many children and grandchildren have spouses.  We might have to simply assume that they all do.

There are six groups of people mentioned here.  We have Old Mrs. Moore, Children, Children's Spouses, Grandchildren, Grandchildren's Spouses, and Great-Grandchildren.  Old Mrs. Moore is just one person.  Let's call the rest of the groups A, B, C, D & E, in that order.

1) Everyone attended, so

1 + A + B + C + D + E = 86

2) three times as many grandchildren as children means

3A = C

3) three times as many great-grand as grand means

3C = E

4) and we're just guessing that each child has a spouse

A=B

5) and also guessing that each grandchild has a spouse

C=D

Subtract out the 1

A + B + C + D + E = 85

Substitute 3C for E in the first equation because of 3)

A + B + C + D + 3C = 85

A + B + 4C + D =85

Substitute C for D because of 5)

A + B + 4C + C = 85

A + B + 5C = 85

Substitute 3A for C becasue of 2)

A + B + 5(3A) = 85

A + B + 15A = 85

16A + B = 85

Finally, substitute A for B because of 4)

16A + A = 85

17A = 85

A = 5

Let's see if we can check our answer

1 + A + B + C + D + E = 86

If Children is 5, Children's Spouses is 5

if Children is 5, Grandchildren is 15

If Grandchildren is 15, Granchildren Spouses is 15

If Grandchildren is 15, Great-Grandchildren is 45

1 + 5 + 5 + 15 + 15 + 45 = 86

Bingo.