SOLUTION: A group of children share some dougnuts.if each child gets 4 pieces, there will be 2 extra doughnuts. if each child get 5 pieces, there will be 4 doughnuts short. how many doughnut

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Question 844535: A group of children share some dougnuts.if each child gets 4 pieces, there will be 2 extra doughnuts. if each child get 5 pieces, there will be 4 doughnuts short. how many doughnuts are there?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the number of doughnuts
Let +c+ = the number of children
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(1) +d%2Fc+=+4+%2B+2%2Fc+ doughnuts/child
(2) +d%2Fc+=+5+-+4%2Fc+ doughnuts/child
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(1) +d+=+4c+%2B+2+
(2) +d+=+5c+-+4+
By substitution:
+4c+%2B+2+=+5c+-+4+
+c+=+6+
and
(1) +d+=+4c+%2B+2+
(1) +d+=+4%2A6+%2B+2+
(1) +d+=+26+
There are 26 doughnuts
check:
(2) +d%2Fc+=+5+-+4%2Fc+
(2) +26%2F6+=+5+-+4%2F6+
(2) +26+=+30+-+4+
(2) +26+=+26+
and
(1) +d%2Fc+=+4+%2B+2%2Fc+
(1) +26%2F6+=+4+%2B+2%2F6+
(1) +26+=+24+%2B+2+
(1) +26+=+26+
OK