r + c = 80 --- there is a total of 80 flowers consisting of roses and carnations
.50r + .10c = 20 -- 50 cent roses + 10 cent carnations = 20 bucks
now we can rearrange equation 1 to single out a variable..
r + c = 80
r = 80 - c
now we can sub 80 - c in for r in the 2nd equation
.50r + .10c = 20
.50(80 - c) + .10c = 20 -- distribute through the parenthesis
40 - .50c + .10c = 20 -- subtract 40 from both sides
-.50c + .10c = 20 - 40 -- combine like terms
-.40c = -20 -- divide both sides by -.40
c = -20/-.40
c = 50
now sub 50 in for c in the 1st equation
r + c = 80
r + 50 = 80
r = 80 - 50
r = 30
check..
.50r + .10c = 20
.50(30) + .10(50) = 20
15 + 5 = 20
20 = 20 (correct)
so the roses (r) = 30 and the carnations (c) = 50
