SOLUTION: Mrs Sabado is 6 times as old as her daughter May. Next year her age will be equal to the square of her daughter's age. Find the present age.

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Question 529334: Mrs Sabado is 6 times as old as her daughter May. Next year her age will be equal to the square of her daughter's age. Find the present age.
Found 2 solutions by oberobic, josmiceli:
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
x = Mrs. Sabado's age
d = her daughter's age
.
x = 6d
.
next year
x+1 = (d+1)^2
.
substitute
.
6d+1 = d^2 + 2d + 1
d^2 -4d = 0
d(d-4) = 0
d = 0 or 4
.
d = 4 = daughter's age
x = 24 = Mrs. Sabado's age
.
Check for next year.
d = 4+1 = 5
d^2 = 25
Which is how old Mrs. Sabado will be.
.
Answer: Mrs. Sabado is 24 and her daughter is 4.
.
Done.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Mrs. Sabado's age now
Let +b+ = May's age now
given:
(1) +a+=+6b+
(2) +a+%2B+1+=+%28+b+%2B+1%29%5E2+
----------------------
(2) +a+%2B+1+=+b%5E2+%2B+2b+%2B+1+
Substitute (1) into (2)
(2) +6b+%2B+1+=+b%5E2+%2B+2b+%2B+1+
(2) +b%5E2+-+4b+=+0+
(2) +b%2A%28+b+-+4+%29+=+0+
Either +b+=+0+ or +b+=+4+
If b+=+4,
(1) +a+=+6b+
(1) +a+=+24+
------------
If +b=0+, then
(1) +a+=+6b+
(1) +a+=+0+
This says they are both newborns, which
is impossible, so
24 is Mrs. Sabado's age now
4 is May's age now
check:
(2) +a+%2B+1+=+%28+b+%2B+1%29%5E2+
(2) +24+%2B+1+=+%28+4+%2B+1%29%5E2+
(2) +25+=+5%5E2+
(2) +25+=+25+
OK