(a) Two different unit rates using this relationship can be:
1) 27 pieces of dark chocolate : 9 pieces of milk chocolate
Simplifying the ratio by dividing both parts by 27, we get:
1 piece of dark chocolate : 1/3 piece of milk chocolate
2) Alternatively, we can multiply the ratio by 3 to get:
27 pieces of dark chocolate : 9 pieces of milk chocolate
= 81 pieces of dark chocolate : 27 pieces of milk chocolate
(b) If 30 pieces of dark chocolate are used, we can find the number of pieces of milk chocolate needed by using the ratio.
Given ratio: 27 pieces of dark chocolate : 9 pieces of milk chocolate
Since the ratio is equal, we can set up a proportion.
27 pieces of dark chocolate / 9 pieces of milk chocolate = 30 pieces of dark chocolate / x pieces of milk chocolate
Simplifying the proportion, we get:
3 pieces of dark chocolate / 1 piece of milk chocolate = 10 pieces of dark chocolate / x pieces of milk chocolate
To solve for x, we can cross multiply:
3x = 10
x = 10/3
Therefore, 10/3 pieces of milk chocolate are needed if 30 pieces of dark chocolate are used.