SOLUTION: Please help me solve this word problem: Dear Action Reporter: If I give each of my children 11 cents, I'll have 9 cents left. If I had 47 cents more, I could give 15 cents to

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Question 670548: Please help me solve this word problem:
Dear Action Reporter:
If I give each of my children 11 cents, I'll have 9 cents left. If I had 47 cents more, I could give 15 cents to each. I can't count my money or my kids, and my pocket calculator is on the fritz. I don't know what to do.

Old Woman in Shoe.
How much money and how many children has the Old Woman?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of children she has
Let +A+ = the amount of money she has
--------------------------------
In the 1st case, she gives her children:
(1) A+=++.11n+%2B+.09+
In the 2nd case, she gives them each:
(2) +%28+A+%2B+.47+%29+%2F+n+=+.15+
------------------------
(2) +A+%2B+.47+=+.15n+
(2) +A+=+.15n+-+.47+
substitute (1) into (2)
(2) +.11n+%2B+.09+=+.15n+-+.47+
(2) +.04n+=+.56+
(2) +n+=+14+
She has 14 children
and
(1) A+=++.11%2A14+%2B+.09+
(1) +A+=+1.54+%2B+.09+
(1) +A+=+1.63+
She has $1.63
check answer:
+1.63+%2F+14+=+.11+%2B+.09%2F14+
+1.63+=+1.54+%2B+.09+
+1.63+=+1.63+
--------------
(2) +A+%2B+.47+=+.15n+
(2) +1.63+%2B+.47+=+.15%2A14+
(2) +2.1+=+2.1+
OK