Astamp 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?

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
 
x + y + z = 160
y = 3 x
5 x + 15 y + 25 z = 2500  / : 5

x + 3 x + z = 160
x + 3 y + 5 z = 500

4 x + z = 160    / * ( - 1 )
10 x + 5 z = 500  / : 5

- 4 x - z = - 160
+
  2 x + z =  100

- 2 x = - 160
x = 30,  y = 90
z = 160 - 120 = 40

-  30 of 5 c stamps,
-  90 of 15 c stamps,
-  40 of 25 c stamps.