Question

esson 5 - 1 understand ratios
quick review
a ratio is a relationship in which for every x units of one quantity there are y units of another quantity. a ratio can be written using the word “to,” a colon, or a fraction bar to separate the two terms.
example
the ratio of men to women at a small wedding is 6:4. if there are 16 women at the wedding, how many men are at the wedding?
draw a diagram to represent the ratio. because 4 boxes represent 16 women, each box represents 4 women.
there are 24 men at the wedding.
practice
a florist uses 5 red roses for every 2 white roses in her bouquets.

1. write the ratio of white roses to red roses in three different ways.
2. write the ratio of red roses to the total number of flowers in three different ways.
3. if the florist uses 10 red roses in a bouquet, how many white roses does she use?
4. if the florist uses 10 white roses in an arrangement, how many red roses does she use?

Explanation:

Step1: Find ratio of white to red roses

The florist uses 5 red roses for every 2 white roses. So the ratio of white roses to red roses is 2:5, 2 to 5, and $\frac{2}{5}$.

Step2: Find ratio of red roses to total flowers

The total number of flowers in the ratio - based combination is $2 + 5=7$. The ratio of red roses to total flowers is 5:7, 5 to 7, and $\frac{5}{7}$.

Step3: Calculate white - roses when red roses are 10

The ratio of white to red roses is 2:5. Let the number of white roses be $x$. We have the proportion $\frac{x}{10}=\frac{2}{5}$. Cross - multiply: $5x = 2\times10$, so $5x=20$ and $x = 4$.

Step4: Calculate red roses when white roses are 10

The ratio of white to red roses is 2:5. Let the number of red roses be $y$. We have the proportion $\frac{10}{y}=\frac{2}{5}$. Cross - multiply: $2y=10\times5$, so $2y = 50$ and $y = 25$.

Answer:

1. 2:5, 2 to 5, $\frac{2}{5}$
2. 5:7, 5 to 7, $\frac{5}{7}$
3. 4
4. 25