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?

Answer 1

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}.