SOLUTION: the father + the mother+ the sister+ the brother = 100 years old. The father squared equals the mother squared plus the sister squared plus the brother squared. The sister

F+M+S+B = 100

F² = M²+S²+B²

S = B-1

We have the equations:

F+M+S+B = 100
F² = M²+S²+B²
S = B-1

Substitute B-1 for S in the first two:

F+M+B-1+B = 100
F² = M²+(B-1)²+B²

Simplify the first:
F+M+2B = 101
F = 101-M-2B

Simplify the second:

F² = M²+S²+(B-1)²
F² = M²+B²-2B+1+B²
F² = M²+2B²-2B+1

Substitute 101-M-2B for F

(101-M-2B)² = M²+2B²-2B+1

Simplify
4B^2+4BM-404B+M^2-202M+10201 = M²+2B²-2B+1

10201+M^2+4B^2-202M-404B+4BM = M²+2B²-2B+1

2B^2+4BM-402B-202M+10200 = 0

Solve that for M:

4BM-202M = 2B^2-402B+10200 

Divide through by 2

2BM-101M = B^2-201B+5100

Factor out M on the left

M(2B-100) = B^2-201B+5100



Now with your TI-83 or 84 calculator, put

  as Y1

Press 2ND WINDOW (for TBLST)

Set TblStart=0 and ΔTbl=1 highlight Auto both places

Press 2ND GRAPH (for TABLE)

Using the down arrow key, scroll down the X column until 
you find a whole number under the Y1 column.

You find that when you get to 14 under the column X,
where you read 34 under Y1.

So that means that B=14 and M=34

Substitute that in F = 101-M-2B
                   F = 101-34-2(14) 
                   F = 39

Then substitute B=14 in S = B-1
                        S = 14-1
                        S = 13

So the father is 39, the mother is 34,
the brother is 14, and the sister is 13.

Edwin