SOLUTION: An account executive bought 330 stamps for $79.50. The purchase included $.15 stamps, $.20 stamps, and $.40 stamps. The number of $.20 stamps is four times the number of $.15 stamp

Question 83935: An account executive bought 330 stamps for $79.50. The purchase included $.15 stamps, $.20 stamps, and $.40 stamps. The number of $.20 stamps is four times the number of $.15 stamps. How many $.40 stamps were purchased?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = no. of .15 stamps; y = no. of .20 stamps; z = no. of .40 stamps
:
Write two equations from this information:
An account executive bought 330 stamps for $79.50.
1st eq: x + y + z = 330
and
2nd eq: .15x + .20y + .40z = 79.50
:
The number of $.20 stamps is four times the number of $.15 stamps.
y = 4x
:
Substitute 4x for y in the 1st equation:
x + 4x + z = 330
5x + z = 330
z = (330 - 5x);
:
In the 2nd equation, substitute 4x for y and (330-5x) for z; find x:
:
.15x + .20(4x) + .40(330-5x) = 79.50
.15x + .80x + 132 - 2x = 79.50
.15x + .80x - 2x = 79.50 - 132
-1.05x = -52.5
x = -52.5/-1.05
x = 50 ea .15 stamps
:
y = 4x
y = 4(50)
y = 200 ea .20 stamps
:
How many $.40 stamps were purchased?
Use the total number of stamps purchased:
:
330 - 50 - 200 = 80 ea .40 stamps
:
:
Check solutions using the 2nd equation:
.15(50) + .20(200) + .40(80) = 79.50
:
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