Three bouquets of flowers are ordered at a florist. 3 roses, 2 carnations, and 1 tulip cost $14. 6 roses, 2 carnations, and 6 tulips cost $38. 1 rose, 12 carnations, and 1 tulip cost $18. how much does each item cost?

cost of 1 rose = $ 3

cost of 1 carnation = $ 1

cost of 1 tulip = $ 3

Solution:

Let "r" be the cost of 1 rose

Let "c" be the cost of 1 carnation

Let "t" be the cost of 1 tulip

3 roses, 2 carnations, and 1 tulip cost $14

So we can frame a equation as:

3 roses x cost of 1 rose + 2 carnations x cost of 1 carnation + 1 tulip x cost of 1 tulip = $ 14

3r + 2c + 1t = 14 ----- eqn 1

6 roses, 2 carnations, and 6 tulips cost $38

So we can frame a equation as:

6 roses x cost of 1 rose + 2 carnations x cost of 1 carnation + 6 tulip x cost of 1 tulip = $ 38

6r + 2c + 6t = 38 ------ eqn 2

1 rose, 12 carnations, and 1 tulip cost $18

So we can frame a equation as:

1 rose x cost of 1 rose + 12 carnations x cost of 1 carnation + 1 tulip x cost of 1 tulip = $ 18

r + 12c + t = 18 ----- eqn 3

Let us solve eqn 1 and eqn 2 and eqn 3 to find values of "r" "c" "t"

3r + 2c + 1t = 14 ----- eqn 1

6r + 2c + 6t = 38 ------ eqn 2

r + 12c + t = 18 ----- eqn 3

From eqn 1,

3r = 14 - 2c - t

Substitute the above value of r in eqn 2

Substitute c = 2t - 5 and in eqn 3

Substitute t = 3 in c = 2t - 5

c = 2(3) - 5

Substitute t = 3 and c = 1 in

Summarizing the results:

cost of 1 rose = $ 3

cost of 1 carnation = $ 1

cost of 1 tulip = $ 3