Question

complete the parts below. write your answers as whole numbers or fractions in simplest form.

(a) a candy shop uses a ratio of 27 pieces of dark chocolate to 9 pieces of milk chocolate when assembling boxes of fudge. give two different unit rates using this relationship.

one unit rate: □ select for each select
another unit rate: □ select for each select

(b) how many pieces of milk chocolate are needed if 30 pieces of dark chocolate are used?

□ pieces of milk chocolate

Explanation:

Part (a)

Step1: Find dark chocolate per milk chocolate

To find the unit rate of dark chocolate per milk chocolate, divide the number of dark chocolate pieces by milk chocolate pieces. So, $\frac{27}{9} = 3$. So, 3 pieces of dark chocolate for each 1 piece of milk chocolate.

Step2: Find milk chocolate per dark chocolate

To find the unit rate of milk chocolate per dark chocolate, divide the number of milk chocolate pieces by dark chocolate pieces. So, $\frac{9}{27} = \frac{1}{3}$. So, $\frac{1}{3}$ piece of milk chocolate for each 1 piece of dark chocolate.

Step1: Determine the ratio

From part (a), the ratio of dark chocolate to milk chocolate is $27:9$ which simplifies to $3:1$ (dark : milk) or the ratio of milk to dark is $\frac{1}{3}$.

Step2: Calculate milk chocolate for 30 dark

If we have 30 dark chocolate pieces, let the number of milk chocolate pieces be $x$. Using the ratio of milk to dark ($\frac{x}{30}=\frac{1}{3}$), we solve for $x$ by cross - multiplying: $3x = 30\times1$, so $x=\frac{30}{3}=10$.

Answer:

One unit rate: $\boldsymbol{3}$ pieces of dark chocolate for each $\boldsymbol{1}$ piece of milk chocolate
Another unit rate: $\boldsymbol{\frac{1}{3}}$ piece of milk chocolate for each $\boldsymbol{1}$ piece of dark chocolate

Part (b)