Question 1103997
let a = 41 cent stamps
let b = 58 cent stamps
let c = 75 cent stamps
:
write an equation for each statement
;
"Kimberly bought 90 stamps"
a + b + c = 90
 three times as many 41 cent stamps as 58 cent stamps
a = 3b
 and that the total cost of the stamps was $43.70."
.41a + .58b + .75c = 43.70
 How many stamps of each denomination did she buy?
:
Replace a with 3b in the first equation
3b + b + c = 90
4b + c = 90
c = (90-4b)  use this for substitution in the 3rd equation
.41a + .58b + .75c = 43.70
.41a + .58b + .75(90-4b) = 43.70
.41a + .58b + 67.5 - 3b = 43.70
combine like terms
.41a - .58b - 3b = 43.70 - 67.50
.41a - 2.42b = -23.80
replace a with 3b
.41(3b) - 2.42b = -23.80
1.23b -2.42b = -23.80
-1.19b = -23.80
b = -23.80/-1.19
b = +20 ea .58 cent stamps
then
3*20 = 60 ea .41 cent stamps
and
90 - 20 - 60 = 10 ea .75 cent stamps
:
:
Check this in the 3rd equation
.41(60) + .58(20) + .75(10) = 
24.60 + 11.69 + 7.50 = 43.70