SOLUTION: a boy was sent to the pst office with $16.25 to buy 2, 3, and 5 cent stamps. he bough 50 mre 3 cent stamps than 2 cent stamps and 25 less 5cent stampsthan 2 cent stamps. how many f

Algebra ->  Real-numbers -> SOLUTION: a boy was sent to the pst office with $16.25 to buy 2, 3, and 5 cent stamps. he bough 50 mre 3 cent stamps than 2 cent stamps and 25 less 5cent stampsthan 2 cent stamps. how many f      Log On


   



Question 280059: a boy was sent to the pst office with $16.25 to buy 2, 3, and 5 cent stamps. he bough 50 mre 3 cent stamps than 2 cent stamps and 25 less 5cent stampsthan 2 cent stamps. how many f each kind did he buy?
if someone can please help me understnd how to do this question it will be greatly appraicated.

Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Set-Up
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Let A = 2 Cent stamps
Let B = 3 Cent stamps
Let C = 5 Cent stamps
Notice that each statement is in terms of the 2 cent stamps.
Equation 1: A+%2B+50+=+B
Equation 2: A+-+25+=+C
Equation 3: 0.02A+%2B+0.03B+%2B+0.05C+=+16.25
Solution
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Use substitution.
Substitute equation 1 and 2 into equation 3
Equation 3: 0.02A+%2B+0.03B+%2B+0.05C+=+16.25
0.02A+%2B+0.03%2A%28A+%2B+50%29+%2B+0.05%2A%28A+-+25%29+=+16.25 Simplify
0.02A+%2B+0.03A+%2B+1.5+%2B+0.05A+-+1.25+=+16.25 Combine like terms
0.1A+%2B+0.25+=+16.25 subtract 0.25 from both sides
0.1A+=+16 Divide both sides by 0.1
highlight%28A+=+160%29
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Now plug 160 into equations 1 & 2 for A
Equation 1: A+%2B+50+=+B
160+%2B+50+=+B
highlight%28210+=+B%29
Equation 2: A+-+25+=+C
160+-+25+=+C
highlight%28135+=+C%29
Check the answers:
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You can check your answers by plugging in the values into equation 3
Equation 3: 0.02A+%2B+0.03B+%2B+0.05C+=+16.25
0.02%2A%28160%29+%2B+0.03%2A%28210%29+%2B+0.05%2A%28135%29+=+16.25
3.2+%2B+6.3+%2B+6.75+=+16.25
highlight%2816.25+=+16.25%29