mrs chan baked some cupcakes. She gave 1/6 of the cupcakes to her neighbour and 7/10 of this remaining cupcakes to
her sister. If she had 12 cupcakes left, how many cupcakes did she bake together?
n cupcskes
n/6 to neighbor , 5n/6 remain
(7/10)(5n/6) to sister or 7n/12 to sister
(3/10)(5n/6) remain or n/4 remain
so
n/4 =12
n =48
To find out how many cupcakes Mrs. Chan baked together, we need to work backwards.
Step 1: Find out how many cupcakes Mrs. Chan had before giving any away.
Since Mrs. Chan had 12 cupcakes left after giving some to her neighbor and sister, we need to reverse the process.
Step 2: Determine how many cupcakes Mrs. Chan had after giving 7/10 of the remaining cupcakes to her sister.
Let's represent the number of cupcakes Mrs. Chan had initially (before giving any away) as "x."
After giving 1/6 of the cupcakes to her neighbor, Mrs. Chan had 5/6 of the cupcakes remaining, which is (5/6)x.
Then, after giving 7/10 of the remaining cupcakes to her sister, Mrs. Chan had (3/10)(5/6)x = (15/60)x = (1/4)x cupcakes left.
Step 3: Use the given information to determine the value of (1/4)x.
Since we know that (1/4)x = 12, we can solve for x by multiplying both sides of the equation by 4:
(1/4)x * 4 = 12 * 4,
x = 48.
Therefore, Mrs. Chan initially baked 48 cupcakes.