Eloise baked some cupcakes. She gave 1 9 of the cupcakes to her friend. She sold 3 4 of the remainder andher family ate the rest. If her family ate 28 cupcakes, how many cupcakes did she bake?
If Eloise's family ate 28 cupcakes, then the 3/4 of the remainder after giving some to her friend is equal to 28 cupcakes.
3/4 of the remainder is 28 cupcakes, so the total number of cupcakes remaining after selling is 4/4 - 3/4 = 1/4.
If 1/4 represents 28 cupcakes, then 100% (which represents the total number of cupcakes she baked) is equal to 4 * 28 = 112 cupcakes. Answer: \boxed{112}.
Let's break down the information step-by-step:
1. Eloise gave away 1/9 of the cupcakes, which means she kept 8/9 of the cupcakes.
2. She sold 3/4 of the remaining cupcakes, so she kept 1 - (3/4) = 1/4 of the cupcakes.
3. Her family ate the rest, which means they ate 28 cupcakes.
Now, we can solve for the total number of cupcakes Eloise baked:
8/9 * 1/4 * Total cupcakes = 28
To get rid of the fractions, we can multiply both sides of the equation by the denominators:
8/9 * 1/4 * Total cupcakes = 28
(8/9) * (1/4) * Total cupcakes = 28 * (9/8) * (4/1)
Total cupcakes = 28 * (9/8) * (4/1) / (8/9) * (1/4)
Total cupcakes = 63
Therefore, Eloise baked 63 cupcakes.
To find out how many cupcakes Eloise baked, we need to work backwards.
We know that her family ate the remainder of the cupcakes after she gave 1/9 of them to her friend and sold 3/4 of the remainder. So, let's start with the number of cupcakes her family ate, which is 28.
Her family ate all the remaining cupcakes, so let's say the number of cupcakes after she sold 3/4 of them is x.
Since her family ate 28 cupcakes, we have the equation x = 28.
Now, let's find the number of cupcakes before she sold 3/4 of them. We can represent this number as y.
To find y, we need to undo the operation of selling 3/4 of the cupcakes. To do that, we need to divide x by 1 - 3/4, which is 1/4.
So, y = x / (1 - 3/4) = x / (1/4) = 4x.
Substituting x = 28, we find that y = 4 * 28 = 112.
Therefore, Eloise baked 112 cupcakes.