Joelle ordered 12 dozen doughnuts for the honor roll breakfast at the middle school.
• 3/8
of the doughnuts have chocolate icing.
• 1/4
of the doughnuts have white icing with sprinkles.
• 1/6
of the doughnuts have pink icing.
• The rest are plain glazed doughnuts.
How many doughnuts are plain glazed doughnuts?
Responses
A 114
B 76
C 54
D 30
To find out how many doughnuts are plain glazed, we need to subtract the number of doughnuts with chocolate icing, white icing with sprinkles, and pink icing from the total number of doughnuts.
3/8 of the doughnuts have chocolate icing, which is (3/8) * 12 dozen = 3 * 12 = <<3/8*12=4.5>>4.5 dozen doughnuts.
1/4 of the doughnuts have white icing with sprinkles, which is (1/4) * 12 dozen = 3 dozen doughnuts.
1/6 of the doughnuts have pink icing, which is (1/6) * 12 dozen = 2 dozen doughnuts.
Therefore, the total number of doughnuts with icing is 4.5 + 3 + 2 = 9.5 dozen doughnuts.
Since there are 12 dozen doughnuts in total, the number of plain glazed doughnuts is 12 - 9.5 = 2.5 dozen doughnuts.
Since there are 12 doughnuts in a dozen, 0.5 dozen is equal to 0.5 * 12 = 6 doughnuts.
Therefore, the number of plain glazed doughnuts is 2.5 dozen * 12 doughnuts/dozen = 30 doughnuts.
The answer is D) 30
To find the number of plain glazed doughnuts, we need to subtract the number of doughnuts with chocolate icing, white icing with sprinkles, and pink icing from the total number of doughnuts.
First, we need to convert the fractions to have a common denominator. The common denominator for 8, 4, and 6 is 24.
• 3/8 can be written as (3/8) × (3/3) = 9/24
• 1/4 can be written as (1/4) × (6/6) = 6/24
• 1/6 can be written as (1/6) × (4/4) = 4/24
Now, let's find the number of plain glazed doughnuts:
Total number of doughnuts = 12 dozen = 12 * 12 = 144
Number of doughnuts with chocolate icing = (9/24) * 144 = 9 * 6 = 54
Number of doughnuts with white icing with sprinkles = (6/24) * 144 = 6 * 6 = 36
Number of doughnuts with pink icing = (4/24) * 144 = 4 * 6 = 24
Number of plain glazed doughnuts = Total number of doughnuts - (Number of doughnuts with chocolate icing + Number of doughnuts with white icing with sprinkles + Number of doughnuts with pink icing) = 144 - (54 + 36 + 24) = 144 - 114 = 30
So, the answer is D) 30.
To find the number of plain glazed doughnuts, we need to subtract the number of doughnuts with chocolate icing, white icing with sprinkles, and pink icing from the total number of doughnuts.
First, let's find the number of doughnuts with chocolate icing:
3/8 of the doughnuts have chocolate icing.
To find this number, we need to multiply 3/8 by the total number of doughnuts:
(3/8) * 12 dozen = 36 dozen
Since there are 12 doughnuts in a dozen, we can convert 36 dozen to 432 doughnuts.
Next, let's find the number of doughnuts with white icing and sprinkles:
1/4 of the doughnuts have white icing with sprinkles.
Using the same process as before:
(1/4) * 12 dozen = 3 dozen
Converting 3 dozen to doughnuts gives us 36 doughnuts.
Now, let's find the number of doughnuts with pink icing:
1/6 of the doughnuts have pink icing.
(1/6) * 12 dozen = 2 dozen
Converting 2 dozen to doughnuts gives us 24 doughnuts.
Now, we can subtract the total number of doughnuts with different types of icing from the total number of doughnuts:
Total number of doughnuts = 12 dozen * 12 = 144 doughnuts
Number of doughnuts with chocolate icing + Number of doughnuts with white icing and sprinkles + Number of doughnuts with pink icing = 432 + 36 + 24 = 492 doughnuts
Number of plain glazed doughnuts = Total number of doughnuts - Number of doughnuts with different types of icing = 144 - 492 = 54 doughnuts
Therefore, the answer is C) 54.