Sabrina ordered some cupcakes for a party. 1/3 of the cupcakes were
lemon-flavoured, 3/8 were vanilla and 5/7 of the remaining cupcakes were
strawberry-flavoured. The rest were chocolate cupcakes. There were 60
more lemon-flavoured cupcakes than strawberry-flavoured cupcakes.
(a) What fraction of the cupcakes were chocolate?
(b) How many cupcakes did Sabrina order?
To solve this problem, let's break it down step by step.
Let's start with the information given:
1/3 of the cupcakes were lemon-flavored.
3/8 of the cupcakes were vanilla-flavored.
5/7 of the remaining cupcakes were strawberry-flavored.
We also know that there were 60 more lemon-flavored cupcakes than strawberry-flavored cupcakes.
(a) To find the fraction of the cupcakes that were chocolate, we need to determine the fraction of cupcakes that were neither lemon, vanilla, nor strawberry.
To find this fraction, we need to subtract the fractions of lemon, vanilla, and strawberry cupcakes from 1.
Let's calculate the fraction of lemon cupcakes:
1/3
The fraction of vanilla cupcakes:
3/8
To find the fraction of strawberry cupcakes, we need to subtract the fractions of lemon and vanilla cupcakes from 1 (since all the remaining cupcakes are either strawberry or chocolate):
1 - (1/3 + 3/8)
To simplify this fraction, we can find the least common denominator (LCD) of 3 and 8, which is 24:
1 - (8/24 + 9/24) = 1 - 17/24
Now we subtract 17/24 from 1 to find the fraction of cupcakes that were neither lemon, vanilla, nor strawberry:
1 - 17/24 = 24/24 - 17/24 = 7/24
Therefore, 7/24 of the cupcakes were chocolate.
(b) To find the total number of cupcakes Sabrina ordered, we need to use the information given in the problem.
Let's assume that the total number of cupcakes Sabrina ordered is represented by "x."
The fraction of cupcakes that were lemon-flavored is 1/3 of the total:
(1/3) * x
The fraction of cupcakes that were vanilla-flavored is 3/8 of the total:
(3/8) * x
The fraction of cupcakes that were strawberry-flavored, after subtracting the lemon and vanilla cupcakes, is 5/7 of the remaining:
(5/7) * [(1 - (1/3 + 3/8)) * x]
We know that there were 60 more lemon-flavored cupcakes than strawberry-flavored cupcakes:
(1/3) * x - (5/7) * [(1 - (1/3 + 3/8)) * x] = 60
To solve this equation, we can substitute the fraction values we previously calculated:
(1/3) * x - (5/7) * [(1 - 17/24) * x] = 60
Now we can solve for x by simplifying the equation and isolating x.
This process will give the total number of cupcakes Sabrina ordered.
Therefore, the answer to (b) requires further calculation based on the equation provided.