Question

A Florián sells roses for $5 each and carnations for $3 each if she makes a bouquet containing a mixture 15 roses and carnations. And sells it for $61. How many of each flower should she use?

Answer 1

Flower prices (per unit):

Roses: $5

Carnations: $3

The bouquet is made of 15 flowers (roses and carnations). If we have R roses and C carnations, then:

R + C = 15 ...(1)

The total price is $61, so:

5R + 3C = 61 ...(2)

So we have 2 equations and 2 unknowns, so the system of equation is solvable. From equation (1):

C = 15 - R

Replacing this on (2):

5R + 3(15 - R) = 61

Solving for R:

5R + 45 - 3R = 61

2R = 61 - 45

2R = 16

R = 8

So there are 8 roses in the bouquet. To have 15 flowers, there need to be 7 carnations.

Answer:

8 roses

7 carnations