SOLUTION: lynn has 159$ in her purse consisting of 20, 5 and 1s'. the number of 20s is the same as the 1s and 5s if she has 14 bills how many of each does she have?

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Question 600618: lynn has 159$ in her purse consisting of 20, 5 and 1s'. the number of 20s is the same as the 1s and 5s if she has 14 bills how many of each does she have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of 1's
Let +b+ = number of 5's
Let +c+ = number of 20's
given:
(1) +c+=+a+%2B+b+
(2) +a+%2B+b+%2B+c+=+14+
(3) +1a+%2B+5b+%2B+20c+=+159+
------------------------
Substitute (1) into (2) and
(1) into (3)
(2) +a+%2B+b+%2B+a+%2B+b+=+14+
(2) +2a+%2B+2b+=+14+
(2) +a+%2B+b+=+7+
and
(3) +1a+%2B+5b+%2B+20%2A%28+a+%2B+b+%29+=+159+
(3) +1a+%2B+5b+%2B+20a+%2B+20b+%29+=+159+
(3) +21a+%2B+25b+=+159+
Multiply both sides of (2) by +21+
and subtract (2) from (3)
(3) +21a+%2B+25b+=+159+
(2) +-21a+-+21b+=+147+
+4b+=+12+
+b+=+3+
and
(2) +a+%2B+b+=+7+
(2) +a+%2B+3+=+7+
(2) +a+=+4+
and
(1) +c+=+a+%2B+b+
(1) +c+=+4+%2B+3+
(1) +c+=+7+
She has 4 ones, 3 fives, and 7 twenties
check:
(3) +1a+%2B+5b+%2B+20c+=+159+
(3) +1%2A4+%2B+5%2A3+%2B+20%2A7+=+159+
(3) +4+%2B+15+%2B+140+=+159+
(3) +159+=+159+
OK