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Hannah works at Blooming Bouquets flower shop. She uses 2 roses for every 5 carnations in the Spring Medley bouquets. Today she will make a Spring Medley bouquet with 16 roses.
How many carnations should Hannah use in the bouquet?

Hannah works at Blooming Bouquets flower shop. She uses $2$ roses for every $5$ carnations in the Spring Medley bouquets. Today she will make a Spring Medley bouquet with $16$ roses. $\newline$ How many carnations should Hannah use in the bouquet?

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Solve proportions: word problems

Full solution

Q. Hannah works at Blooming Bouquets flower shop. She uses

2

roses for every

5

carnations in the Spring Medley bouquets. Today she will make a Spring Medley bouquet with

16

roses.

\newline

How many carnations should Hannah use in the bouquet?

Identify Ratio: Identify the ratio of roses to carnations in the Spring Medley bouquets. Hannah uses $2$ roses for every $5$ carnations.
Determine Roses: Determine the number of roses Hannah will use in the bouquet. Hannah will use $16$ roses in the bouquet.
Calculate Carnations: Calculate the number of carnations needed for the bouquet based on the given ratio. $\newline$ Since the ratio is $2$ roses to $5$ carnations, we can set up a proportion to find the number of carnations: $\newline$ $\frac{2 \text{ roses}}{5 \text{ carnations}} = \frac{16 \text{ roses}}{x \text{ carnations}}$
Solve Proportion: Solve the proportion for $x$ to find the number of carnations. $\frac{2}{5} = \frac{16}{x}$ Cross-multiply to solve for $x$ : $2 \times x = 5 \times 16$ $2x = 80$ $x = \frac{80}{2}$ $x = 40$
Verify Solution: Verify that the solution makes sense in the context of the problem. $\newline$ If $2$ roses correspond to $5$ carnations, then $16$ roses (which is $8$ times more) should correspond to $8$ times more carnations, which is $40$ carnations. This makes sense with the ratio given.

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