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?
:
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/6}}}; 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/6}}} for z in above equation
.20(3y) + .10y + .05*{{{y/6}}} = 63.75
:
.6y + .1y + {{{(.05y)/6}}} = 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 = {{{382.5/4.25}}}
y = 90 ea 10 cent stamps
then
z = {{{90/6}}}
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