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)

Step 1: Find the first unit rate (dark chocolate per milk chocolate)

The ratio of dark chocolate to milk chocolate is \(27:9\). To find the unit rate of dark chocolate per 1 piece of milk chocolate, we divide the number of dark chocolate pieces by the number of milk chocolate pieces. So, \(\frac{27}{9} = 3\). So the unit rate is \(3\) pieces of dark chocolate for each \(1\) piece of milk chocolate.

Step 2: Find the second unit rate (milk chocolate per dark chocolate)

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

Part (b)

Step 1: Set up the proportion

We know the ratio of dark chocolate to milk chocolate is \(27:9\) or simplified \(3:1\). Let \(x\) be the number of milk chocolate pieces when there are 30 pieces of dark chocolate. So we set up the proportion \(\frac{27}{9}=\frac{30}{x}\).

Step 2: Cross - multiply and solve for \(x\)

Cross - multiplying gives us \(27x = 30\times9\). First, calculate \(30\times9 = 270\). Then, \(x=\frac{270}{27}=10\).

Answer:

s:
(a) One unit rate: \(3\) pieces of dark chocolate for each \(1\) piece of milk chocolate; Another unit rate: \(\frac{1}{3}\) piece of milk chocolate for each \(1\) piece of dark chocolate.
(b) The number of pieces of milk chocolate needed is \(10\).