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In Sakura's garden, for every 5 red flowers, there are 10 yellow flowers. There are a total of 75 yellow and red flowers in her garden.
How many red flowers are in Sakura's garden?
red flowers

In Sakura's garden, for every $5$ red flowers, there are $10$ yellow flowers. There are a total of $75$ yellow and red flowers in her garden. $\newline$ How many red flowers are in Sakura's garden? $\newline$ red flowers

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Counting principle

Full solution

Q. In Sakura's garden, for every

5

red flowers, there are

10

yellow flowers. There are a total of

75

yellow and red flowers in her garden.

\newline

How many red flowers are in Sakura's garden?

\newline

red flowers

Understanding the Ratio: Understand the ratio of red to yellow flowers and the total number of flowers. $\newline$ Sakura's garden has a ratio of $5$ red flowers to $10$ yellow flowers. This ratio can be simplified to $1$ red flower for every $2$ yellow flowers. There are a total of $75$ yellow and red flowers in her garden.
Calculating Total Parts: Calculate the total parts of flowers based on the simplified ratio. $\newline$ Since the ratio is $1$ red flower to $2$ yellow flowers, there are $3$ parts in total ( $1$ part red $+$ $2$ parts yellow).
Determining the Value of One Part: Determine the value of one part. $\newline$ To find out how many flowers represent one part, we divide the total number of flowers by the total number of parts. $\newline$ Total number of flowers = $75$ $\newline$ Total parts = $3$ $\newline$ Value of one part = Total number of flowers / Total parts $\newline$ Value of one part = $75 / 3$ $\newline$ Value of one part = $25$
Calculating the Number of Red Flowers: Calculate the number of red flowers. $\newline$ Since $1$ part represents red flowers, we multiply the value of one part by the number of parts for red flowers. $\newline$ Number of red flowers $=$ Value of one part $\times$ Number of parts for red flowers $\newline$ Number of red flowers $= 25 \times 1$ $\newline$ Number of red flowers $= 25$

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