SOLUTION: Victor bought less than $8.40 worth of stamps. He bought 3 times as many 17cent stamps as 25 cent stamps and 4 times as many 2 cent stamps as 25 cent stamps. Find the greatest poss

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Question 791384: Victor bought less than $8.40 worth of stamps. He bought 3 times as many 17cent stamps as 25 cent stamps and 4 times as many 2 cent stamps as 25 cent stamps. Find the greatest possible number of 25 cent stamps he bought.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+%7D%7B%7D%7D+=+total+number+of+stamps+bought%0D%0ALet+%7B%7B%7B+b+ = number of 17 cent stamps bought
Let +c+ = number of 25 cent stamps bought
Let +d+ = number of 2 cent stamps bought
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given:
(1) +a+%3C+840+ ( in cents )
(2) +b+=+3c+
(3) +d+=+4c+
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The number of 17 cent stamps was +3c+, so I
can say +%283c%29%2A17+%2B+25c+%3C+840+
+51c+%2B+25c+%3C+840+
+c+%3C+840+%2F+76+
+c+%3C+11+ and a fraction
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Now I can include the 2 cent stamps
+%284c%29%2A2+%2B+c%2A25+%2B+%283c%29%2A17+%3C+840+
+8c+%2B+25c+%2B+51c+%3C+840+
+84c+%3C+840+
+c+%3C+10+
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So, the most 25 cent stamps is 9
check answer:
+9%2A25+=+225+
+225+%2B+3%2A9%2A17+%2B+4%2A9%2A2+%3C+840+
+225+%2B+459+%2B+72+%3C+840+
+756+%3C+840+
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See if this still hold if there is 1 more 25 cent stamp
+10%2A25+%2B+3%2A10%2A17+%2B+4%2A10%2A2+%3C+840+
+250+%2B+510+%2B+80+%3C+840+
+840+%3C+840+
Not true, so answer is correct