SOLUTION: A stamp collection consists of 3, 8, and 15 cent stamps. The number of 8 stamps is one less than triple the number of 3 cent stamps. The number of 15 cent stamps is six less than

Algebra ->  Expressions-with-variables -> SOLUTION: A stamp collection consists of 3, 8, and 15 cent stamps. The number of 8 stamps is one less than triple the number of 3 cent stamps. The number of 15 cent stamps is six less than      Log On


   

Question 292147: A stamp collection consists of 3, 8, and 15 cent stamps. The number of 8 stamps is one less than triple the number of 3 cent stamps. The number of 15 cent stamps is six less than the number of 8 cent stamps. The total value of all stamps is $2.47. Find the number of 8 cent stamps in the collection
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A stamp collection consists of 3, 8, and 15 cent stamps.
The number of 8 stamps is one less than triple the number of 3 cent stamps.
The number of 15 cent stamps is six less than the number of 8 cent stamps.
The total value of all stamps is $2.47.
Find the number of 8 cent stamps in the collection
:
Let x, y, z = the number of 3, 8, 15 cent stamps respectively
:
"The number of 8 stamps is one less than triple the number of 3 cent stamps."
y = 3x - 1
or
3x = y + 1
x = %28y%2B1%29%2F3
:
"The number of 15 cent stamps is six less than the number of 8 cent stamps."
z = y - 6
:
"The total value of all stamps is $2.47."
.03x + .08y+ .15z = 2.47
Replace x and z
.03(%28y%2B1%29%2F3) + .08y + .15(y-6) = 2.47
Multiply by 3 to get rid of that denominator, results
.03(y+1) + .24y + .45(y-6) = 3(2.47)
:
.03y + .03 + .24y + .45y - 2.7 = 7.41
:
.72y - 2.67 = 7.41
:
.72y = 7.41 + 2.67
:
.72y = 10.08
y = 10.08%2F.72
y = 14 ea 8 cent stamps
:
:
Check our solution:
Find the no. 3 and 15 cent stamps
x = %2814%2B1%29%2F3
x = 5 ea 3 cent stamps
:
z = 14 - 6
z = 8 ea 15 cent stamps
;
.03(5) + .08(14) + .15(8) =
.15 + 1.12 + 1.20 = 2.47