SOLUTION: Mountainside Fleece sold 40 neck warmers. Solid color warmers sold for $9.90 each and colored ones sold for $12.75 each. In all $421.65 was collected. How many of each were sold

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Question 259815: Mountainside Fleece sold 40 neck warmers. Solid color warmers sold for $9.90 each and colored ones sold for $12.75 each. In all $421.65 was collected. How many of each were sold?!
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Let C = colored, and S = solid
We create two equations from the given
(i) S+%2B+C+=+40
(ii) 9.90S+%2B+12.75C+=+421.65
First get rid of the decimals in (ii) and write
(iii) 990S+%2B+1275C+=+42165
--
step 1 - solve (i) for S and we get
(iv) C+=+40-S
step 2 - substitute (iv) into (iii) to get
(v) 990S+%2B+1275%2840-S%29+=+42165
distribute and simplify to get
(vi) -285S+%2B+51000+=+42165
subtract to get
(vii) -285S+=+-8835
divide to get
S+=+31
so, we have
C+=+9