Question

Alice baked a certain number of pies. She gave 1/8 of the pies to her friends and 1/4 of the remainder to her neighbor She was left with 63 pies. How many pies did Alice bake at first?

Answer 1

Original count of pies is 96

Explanation:

Let the original count of pies be represented by `x`

She gave `1/8` of the pies to her friend
Thus for the remainder 'remove' `1/8` of the count `-> x-x/8`

A quarter of this given to the neighbour

So the remainder after this is:

`color(green)((x-x/8)-(x-x/8)/4)`

We are told that this count is 63. So we have:

`color(green)((x-x/8)-(x-x/8)/4 = 63)`
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`color(green)((x-x/8)-(x-x/8)1/4 = 63)`

`color(green)((8x-x)/8-((8x-x)/8)1/4=63)`

`color(green)((7x)/8-(7x)/32=63)`

`color(green)([(7x)/8color(red)(xx1)]-(7x)/32=63 color(white)("dddd") -> color(white)("dddd")[(7x)/8color(red)(xx4/4)]-(7x)/32=63)`

`color(green)((28x)/32-(7x)/32=63`

`color(green)((21x)/32=63`

Multiply both sides by `32/21`

`color(green)(x=32/cancel(21)^1xxcancel(63)^3)`

`color(green)(x=96)`