SOLUTION: Tim bought 3 times as many .20 stamps as .10 stamps and 6 times as many .10 at .05 stamps. He spent $63.75 on stamps. How many of each kind did he buy?

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Question 156225: Tim bought 3 times as many .20 stamps as .10 stamps and 6 times as many .10 at .05 stamps. He spent $63.75 on stamps. How many of each kind did he buy?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Tim bought 3 times as many .20 stamps as .10 stamps and 6 times as many .10 at .05 stamps. He spent $63.75 on stamps. How many of each kind did he buy?
:
Let x, y, z = .20, .10, & .05 stamps respectively
:
Write an equation for each phrase;
"Tim bought 3 times as many .20 stamps as .10 stamps"
x = 3y
;
" and 6 times as many .10 at .05 stamps."
y = 6z
or
z = y%2F6; try to get everything in terms of y
"He spent $63.75 on stamps."
.20x + .10y + .05z = 63.75
:
How many of each kind did he buy?
Substitute 3y for x and y%2F6 for z in above equation
.20(3y) + .10y + .05*y%2F6 = 63.75
:
.6y + .1y + %28.05y%29%2F6 = 63.75
Multiply equation by 6 to get rid of the denominator, results:
3.6y + .6y + .05y = 6(63.75)
4.25y = 382.5
y = 382.5%2F4.25
y = 90 ea 10 cent stamps
then
z = 90%2F6
z = 15 ea 5 cent stamps
and
x = 3*90
x = 270 ea 20 cent stamps
:
:
Check solution in the $total equation:
.2(270) + .1(90) + .05(15) =
54.00 + 9.00 + .75 = 63.75; confirms our solutions