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?

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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?

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Answer 1 · 2018-04-17T20:43:52

Original count of pies is 96

Explanation:

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

She gave $\frac{1}{8}$ $1/8$ of the pies to her friend
Thus for the remainder 'remove' $\frac{1}{8}$ $1/8$ of the count $\to x - \frac{x}{8}$ $-> x-x/8$

A quarter of this given to the neighbour

So the remainder after this is:

$(x - \frac{x}{8}) - \frac{x - \frac{x}{8}}{4}$ $color(green)((x-x/8)-(x-x/8)/4)$

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

$(x - \frac{x}{8}) - \frac{x - \frac{x}{8}}{4} = 63$ $color(green)((x-x/8)-(x-x/8)/4 = 63)$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$(x - \frac{x}{8}) - (x - \frac{x}{8}) \frac{1}{4} = 63$ $color(green)((x-x/8)-(x-x/8)1/4 = 63)$

$\frac{8 x - x}{8} - (\frac{8 x - x}{8}) \frac{1}{4} = 63$ $color(green)((8x-x)/8-((8x-x)/8)1/4=63)$

$\frac{7 x}{8} - \frac{7 x}{32} = 63$ $color(green)((7x)/8-(7x)/32=63)$

$[\frac{7 x}{8} \times 1] - \frac{7 x}{32} = 63 dddd \to dddd [\frac{7 x}{8} \times \frac{4}{4}] - \frac{7 x}{32} = 63$ $color(green)([(7x)/8color(red)(xx1)]-(7x)/32=63 color(white)("dddd") -> color(white)("dddd")[(7x)/8color(red)(xx4/4)]-(7x)/32=63)$

$\frac{28 x}{32} - \frac{7 x}{32} = 63$ $color(green)((28x)/32-(7x)/32=63$

$\frac{21 x}{32} = 63$ $color(green)((21x)/32=63$

Multiply both sides by $\frac{32}{21}$ $32/21$

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

$color(green)(x=96)$

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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?

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Explanation:

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