SOLUTION: Cheryl buys a total of 100 stamps at the post office for $20.56. if che bought 5 cent stamps, 15 cent stamps and 37 cent stamps only, and there were 10 more 37 cent stamps than 5 c

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Cheryl buys a total of 100 stamps at the post office for $20.56. if che bought 5 cent stamps, 15 cent stamps and 37 cent stamps only, and there were 10 more 37 cent stamps than 5 c      Log On


   



Question 885404: Cheryl buys a total of 100 stamps at the post office for $20.56. if che bought 5 cent stamps, 15 cent stamps and 37 cent stamps only, and there were 10 more 37 cent stamps than 5 cent stamps. How many of each did she buy?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of 5 cent stamps
Let +b+ = number of 15 cent stamps
Let +c+ = number of 37 cent stamps
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(1) +a+%2B+b+%2B+c+=+100+
(2) +5a+%2B+15b+%2B+37c+=+2056+ ( in cents )
(3) +c+=+a+%2B+10+
-------------------
Substitute (3) into (1)
(1) +a+%2B+b+%2B+a+%2B+10+=+100+
(1) +2a+%2B+b+=+90+
(1) +b+=+90+-+2a+
----------------------
Substitute (1) into (2)
(2) +5a+%2B+15%2A%28+90+-+2a+%29+%2B+37c+=+2056+
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Substitute (3) into (2)
(2) +5a+%2B+15%2A%28+90+-+2a+%29+%2B+37%2A%28+a+%2B+10+%29+=+2056+
(2) +5a+%2B+1350+-+30a+%2B+37a+%2B+370+=+2056+
(2) +12a+=+2056+-+1350+-+370+
(2) +12a+=+2056+-+1720+
(2) +12a+=+336+
(2) +a+=+28+
and
(1) +b+=+90+-+2a+
(1) +b+=+90+-+2%2A28+
(1) +b+=+34+
and
(3) +c+=+a+%2B+10+
(3) +c+=+38+
She bought 28 of the 5 cent stamps
She bought 34 of the 15 cent stamps
She bought 38 of the 37 cent stamps
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check:
(2) +5a+%2B+15b+%2B+37c+=+2056+
(2) +5%2A28+%2B+15%2A34+%2B+37%2A38+=+2056+
(2) +140+%2B+510+%2B+1406+=+2056+
(2) +2056+=+2056+
OK