SOLUTION: Show your method used to solve problem. If the cost of 5 roses, 9 irises and 6 carnations is the same as 3 carnations 6 irises and 8 roses find the cost of a single iris if it cos

Question 949379: Show your method used to solve problem.
If the cost of 5 roses, 9 irises and 6 carnations is the same as 3 carnations 6 irises and 8 roses find the cost of a single iris if it cost $42 for a dozen roses and a carnation is three-quarters the cost of an iris.
Found 3 solutions by macston, MathTherapy, lwsshak3:
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
I=cost of iris; C=cost of carnation=0.75I; R=cost of rose=$42/12=$3.50
5R+9I+6C=3C+6I+8R Substitute for C and R.
5($3.5)+9I+6(0.75I)=3(0.75I)+6I+8($3.5)
$17.50+9I+$4.50I=2.25I+6I+$28.00 Subtract $17.50 from each side.
$13.50I=$8.25I+$10.50 Subtract $8.25I from each side.
$5.25I=$10.50 Divide each side by $5.25.
I=$2.00 ANSWER: An iris costs $2.00.
CHECK:
C=0.75I=0.75($2)=$1.50 A carnation costs $1.50.
5R+9I+6C=3C+6I+8R
5($3.50)+9($2.00)+6($1.50)=3($1.50)+6($2.00)+8($3.50)
$17.50+$18.00+$9.00=$4.50+$12.00+$28.00
$44.50=$44.50

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Show your method used to solve problem.
If the cost of 5 roses, 9 irises and 6 carnations is the same as 3 carnations 6 irises and 8 roses find the cost of a single iris if it cost $42 for a dozen roses and a carnation is three-quarters the cost of an iris.

Let price of 1 rose, 1 iris and 1 carnation be R, I, and C, respectively
Then we can say that: 5R + 9I + 6C = 8R + 6I + 3C
8R - 5R + 6I - 9I + 3C - 6C = 0
3R - 3I - 3C = 0
3(R - I - C) = 3(0) ------ Factoring out GCF, 3
R - I - C = 0 ------- eq (i)
12R = 42
R, or cost of 1 rose = , or $3.50
_____ ------- Cost of 1 carnation is cost of an iris
R - I - C = 0 -------- eq (i)
-------- Substituting 3.5 for R, and for C in eq (i)
-------- Multiplying by LCD, 4
14 - 7I = 0
14 = 7I
Cost of 1 iris = , or
Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
Show your method used to solve problem.
If the cost of 5 roses, 9 irises and 6 carnations is the same as 3 carnations 6 irises and 8 roses find the cost of a single iris if it cost $42 for a dozen roses and a carnation is three-quarters the cost of an iris.
***
let r=cost/rose=42/12
let i=cost/iris
let c=cost/carnation=(3/4)i
..
5r+9i+6c=3c+6i+8r
5(42/12)+9i+6(3/4)i=3(3/4)i+6i+8(42/12)
210/12+9i+(18/4)i=(9/4)i+6i+336/12
lcd:12
210+108i+54i=27i+72i+336
63i=126
i=2
cost of a single iris=$2
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