SOLUTION: From a pile of coins containing nickels (N), dimes (D) and quarters (Q), Tom picked 10 coins with a total value of $1.00. The 10 coins had a different huber of each of the three

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Question 1080739: From a pile of coins containing nickels (N), dimes (D) and quarters (Q), Tom picked 10 coins with a total value of $1.00. The 10 coins had a different huber of each of the three types of coins and at least 1 coin of each type. How many coins of each type did he pick?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +10d+%2B+5n+%2B+25q+=+100+
(2) +d+%2B+n+%2B+q+=+10+
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I have to look at 3 cases:
1 quarter
2 quarters
3 quarters
-------------------------
Case 1:
+q+=+1+
The equations are:
(1) +10d+%2B+5n+%2B+25%2A1+=+100+
(2) +d+%2B+n+%2B+1+=+10+
-------------------------
(2) +d+=+9+-+n+
(1) +10%2A%28+9-n+%29+%2B+5n+%2B+25+=+100+
(1) +90+-+10n+%2B+5n+=+75+
(1) +5n+=+15+
(1) +n+=+3+
and
(2) +d+=+9+-+n+
(2) +d+=+9+-+3+
(2) +d+=+6+
----------------------
There are:
1 quarter
3 nickels
6 dimes
I don't have to go any further -this solves it
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check:
(1) +10d+%2B+5n+%2B+25q+=+100+
(1) +10%2A6+%2B+5%2A3+%2B+25%2A1+=+100+
(1) +60+%2B+15+%2B+25+=+100+
(1) +100+=+100+
OK