Casey is making a flower arrangement with roses(r) and carnations(c). the cost of each rose is $0.50 and the cost of each carnation is $0.10. the arrangement has a total of 80 flowers and the flower cost was $20. how many of each flower did casey put in her arrangement?

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