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 dark chocolate are needed if 8 pieces of milk chocolate are used?
(a) Two different unit rates using the given ratio could be:
1. For every 27 pieces of dark chocolate, there are 9 pieces of milk chocolate.
2. For every 3 pieces of dark chocolate, there is 1 piece of milk chocolate.
(b) To find the number of pieces of dark chocolate needed when 8 pieces of milk chocolate are used, we can use the ratio given in part (a):
Using the second unit rate, for every 3 pieces of dark chocolate, there is 1 piece of milk chocolate. So, the ratio can be written as 3:1.
If 1 piece of milk chocolate corresponds to 3 pieces of dark chocolate, then 8 pieces of milk chocolate would correspond to 3 * 8 = 24 pieces of dark chocolate.
Therefore, 24 pieces of dark chocolate are needed if 8 pieces of milk chocolate are used.
for each unit rate there only 1 number to put not 2
(a) A candy shop uses a ratio of 27 pieces of dark chocolate to 9 pieces of milk chocolate when assembling boxes of fudge. Two different unit rates using this relationship can be:
1. For every 27 pieces of dark chocolate, there are 9 pieces of milk chocolate. The unit rate would be 27:9, or simply 3:1 when simplified by dividing both numbers by 9.
2. For every 9 pieces of milk chocolate, there are 27 pieces of dark chocolate. The unit rate would be 9:27, or simply 1:3 when simplified by dividing both numbers by 9.
(b) To find the number of pieces of dark chocolate needed if 8 pieces of milk chocolate are used, we can use the unit rate from part (a) (which was 3:1).
If the unit rate is 3:1, and we have 8 pieces of milk chocolate, then we need to multiply 8 by the denominator of the unit rate (which is 1) to find the corresponding number of dark chocolate.
8 x 3 = 24
Therefore, 24 pieces of dark chocolate are needed if 8 pieces of milk chocolate are used.