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.
(b)How many pieces of milk chocolate are needed if 30 pieces of dark chocolate are used?
(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.
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(a) Two different unit rates using this relationship can be:
1) 27 pieces of dark chocolate : 9 pieces of milk chocolate
To find the unit rate, we can simplify the ratio by dividing both parts by the greatest common divisor, which is 9.
27/9 = 3 pieces of dark chocolate : 1 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 use the unit rate from previous part (1) to find the number of pieces of milk chocolate needed.
3 pieces of dark chocolate : 1 piece of milk chocolate
Since the unit rate is 3 pieces of dark chocolate to 1 piece of milk chocolate, we can set up a proportion:
3 pieces of dark chocolate / 1 piece of milk chocolate = 30 pieces of dark chocolate / x pieces of milk chocolate
To solve for x, we can cross multiply:
3x = 30
x = 30/3
x = 10
Therefore, 10 pieces of milk chocolate are needed if 30 pieces of dark chocolate are used.
(a) To find unit rates, we need to divide the given quantities by one another.
The first unit rate is 27 pieces of dark chocolate to 9 pieces of milk chocolate. Dividing both quantities by 9, we get:
27 ÷ 9 = 3 pieces of dark chocolate to 1 piece of milk chocolate.
So, the first unit rate is 3:1.
The second unit rate can be obtained by dividing both quantities by 27. We get:
27 ÷ 27 = 1 piece of dark chocolate to 1/3 piece of milk chocolate.
To express this as a whole number, we can multiply both numbers by 3 to get:
3:1
So, the second unit rate is 3:1.
(b) If 30 pieces of dark chocolate are used, we can use the unit rate to find the corresponding quantity of milk chocolate.
Using the first unit rate of 3:1, we can set up a proportion:
27 dark chocolate pieces / 9 milk chocolate pieces = 30 dark chocolate pieces / x milk chocolate pieces.
Cross-multiplying, we get:
27x = 9 * 30.
Simplifying the right side of the equation, we have:
27x = 270.
Dividing both sides of the equation by 27, we find:
x = 10.
Therefore, if 30 pieces of dark chocolate are used, 10 pieces of milk chocolate are needed.