Question

A stamp collector bought 160 stamps for $25.00. The purchase included 5¢ stamps, 15¢ stamps, and 25¢ stamps. The number of 15¢ stamps is three times the number of 5¢ stamps. How many of each type of stamp was purchased?

Answer 1

x - number of 5 c stamps,
y - number of 15 c stamps,
z - number of 25 c stamps.
The system:
x + y + z = 160
y = 3 x
0.05 x + 0.15 y + 0.25 z = 25 / * 100
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x + y + z = 160
y = 3 x
5 x + 15 y + 25 z = 2500 / : 5
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x + 3 x + z = 160
x + 3 y + 5 z = 500
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4 x + z = 160 / * ( - 1 )
10 x + 5 z = 500 / : 5
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- 4 x - z = - 160
+
2 x + z = 100
-------------------------
- 2 x = - 160
x = 30, y = 90
z = 160 - 120 = 40
Answer:
- 30 of 5 c stamps,
- 90 of 15 c stamps,
- 40 of 25 c stamps.