Complete the parts below. Write your answers as whole numbers or fractions in simplest form.
(a)A candy shop uses a ratio of 36 pieces of dark chocolate to 12 pieces of milk chocolate when assembling boxes of fudge. Give two different unit rates using this relationship.
One unit rate: for each
Another unit rate: for each
(b)How many pieces of milk chocolate are needed if 42 pieces of dark chocolate are used?
pieces of milk chocolate
(a) One unit rate: 3 pieces of dark chocolate for each 1 piece of milk chocolate
Another unit rate: 12 pieces of dark chocolate for each 4 pieces of milk chocolate
(b) If 42 pieces of dark chocolate are used, then the number of pieces of milk chocolate needed can be found using the ratio:
36 pieces of dark chocolate / 12 pieces of milk chocolate = 42 pieces of dark chocolate / x pieces of milk chocolate
Cross-multiplying, we get:
36x = 12 * 42
36x = 504
Dividing both sides by 36, we get:
x = 504 / 36
x = 14
Therefore, 14 pieces of milk chocolate are needed if 42 pieces of dark chocolate are used.
(a) To find two different unit rates using the given ratio of 36 pieces of dark chocolate to 12 pieces of milk chocolate, we can divide both sides of the ratio by the number of dark chocolates or the number of milk chocolates.
One unit rate: 36 pieces of dark chocolate ÷ 12 pieces of milk chocolate = 3 pieces of dark chocolate per 1 piece of milk chocolate
Another unit rate: 12 pieces of milk chocolate ÷ 36 pieces of dark chocolate = 1/3 piece of milk chocolate per 1 piece of dark chocolate
(b) If 42 pieces of dark chocolate are used, we can use the unit rate to find the number of pieces of milk chocolate needed.
Using the unit rate of 3 pieces of dark chocolate per 1 piece of milk chocolate:
42 pieces of dark chocolate × (1 piece of milk chocolate ÷ 3 pieces of dark chocolate) = 14 pieces of milk chocolate
Therefore, 14 pieces of milk chocolate are needed if 42 pieces of dark chocolate are used.
To find the unit rates, we need to divide the number of dark chocolate pieces by the number of milk chocolate pieces in the ratio.
(a)
The first unit rate can be calculated as:
Number of dark chocolate pieces / Number of milk chocolate pieces = 36 / 12 = 3/1
So, the first unit rate is 3 pieces of dark chocolate for each piece of milk chocolate.
The second unit rate can be calculated by taking the reciprocal of the first unit rate:
Number of milk chocolate pieces / Number of dark chocolate pieces = 12 / 36 = 1/3
So, the second unit rate is 1 piece of milk chocolate for every 3 pieces of dark chocolate.
(b)
To find the number of pieces of milk chocolate needed if 42 pieces of dark chocolate are used, we can use the second unit rate.
Number of milk chocolate pieces = Number of dark chocolate pieces * Second unit rate
Number of milk chocolate pieces = 42 * 1/3 = 14
Therefore, 14 pieces of milk chocolate are needed if 42 pieces of dark chocolate are used.