Eloise baked some cupcakes she gave 1 9 of the cupcakes toher friend she sold 3 4 of the remainder and her family ate the rest if her family ate 28 cupcakes how many cuocakes did she bake?
Let's first find out how many cupcakes she had before giving some to her friend. If her family ate the rest, the number of cupcakes her friend received is 28 cupcakes, so the total number of cupcakes was 28 cupcakes before her friend received some.
Since 3/4 of the remainder was sold, and if we let x represent the number of cupcakes she was left with after giving her friend some, then 3/4 of x was sold
Since her friend received 1/9 of the cupcakes and sold 3/4 of the remainder, then 28 cupcakes + 3/4x = x - 1/9x
Then, 28 cupcakes + 3/4x - x + 1/9x = 0
Then, combining like terms, we get 28 cupcakes - 7/36x = 0
Then, adding 7/36x to both sides, we get 28 cupcakes = 7/36x
Then, dividing both sides by 7/36, we get 36 = 4/9x
Then, multiplying both sides by 9/4 multiplied to both sides, we get 81 = x
Therefore, Eloise baked 81 cupcakes. Answer: \boxed{81}.
Let's break down the problem step by step:
Step 1: Eloise gave 1/9 of the cupcakes to her friend.
So, she had (1 - 1/9) = 8/9 of the cupcakes remaining.
Step 2: Eloise sold 3/4 of the remaining cupcakes.
This means she sold (3/4) * (8/9) = (24/36) = 2/3 of the original number of cupcakes.
Step 3: The family ate the remaining cupcakes.
This means they ate (1 - 2/3) = 1/3 of the original number of cupcakes.
Step 4: It is given that the family ate 28 cupcakes.
So, 1/3 of the original number of cupcakes is equal to 28.
Step 5: Let's find the original number of cupcakes.
To find the original number of cupcakes, we can multiply both sides of the equation by 3: (1/3) * 3 = 28 * 3/1.
This simplifies to 1 = 84/1.
Therefore, the original number of cupcakes Eloise baked is equal to 84.
To find the number of cupcakes Eloise baked, we can follow a step-by-step approach to determine the answer.
Step 1: Calculate the number of cupcakes she gave to her friend.
Let's assume the total number of cupcakes Eloise baked is represented by C. From the problem statement, she gave 1/9 of the cupcakes to her friend. So, the number of cupcakes left after giving to her friend is (C - C/9) cupcakes.
Step 2: Calculate the number of cupcakes Eloise sold.
Out of the remaining cupcakes, she sold 3/4 of them. Using the number of cupcakes left after Step 1, we can calculate the number she sold. So, the number of cupcakes left after selling is [(C - C/9) - (3/4)(C - C/9)] cupcakes.
Step 3: Calculate the number of cupcakes Eloise's family ate.
From the problem, her family ate 28 cupcakes. Using the number of cupcakes left after Step 2, we can find the number of cupcakes her family ate. Therefore, [(C - C/9) - (3/4)(C - C/9)] - 28 = 0 cupcakes.
Now, we can solve the equation to find the value of C, which represents the total number of cupcakes Eloise baked.
Let's calculate the equation:
(C - C/9) - (3/4)(C - C/9) - 28 = 0
Simplifying the equation:
(8/9)C - (9/36)C - (3/4)(8/9)C + (3/4)(9/36)C - 28 = 0
Multiplying and simplifying more:
(8C)/9 - (C)/12 - (24C)/36 + (C)/12 - 28 = 0
Combining like terms:
(35C)/36 - 28 = 0
(35C)/36 = 28
Multiplying both sides by 36:
35C = 28 * 36
C = (28 * 36)/35
Calculating:
C = 28 * 36 = 1008/35
C ≈ 28.8 (approximated to the nearest whole number)
Therefore, Eloise baked approximately 29 cupcakes.