Question 497525
Let {{{x[0]}}} = the number of eggs she starts with
After 1st stop, she has
{{{ x[1] = x[0] - (x[0]/2 + 1/2) }}}
After 2nd stop, she has
{{{ x[2] = x[1] - (x[1]/2 + 1/2) }}}
After 3rd stop, she has
{{{ x[3] = x[2] - (x[2]/2 + 1/2) }}}
After 4th stop, she has
{{{ x[4] = x[3] - (x[3]/2 + 1/2) }}}
After 5th stop, she has
{{{ x[5] = x[4] - (x[4]/2 + 1/2) }}}
It is given that {{{ x[5] }}}, the number of eggs
she ends up with is zero, so
{{{ x[4] - (x[4]/2 + 1/2)  = 0}}}
{{{ x[4] - x[4]/2 - 1/2 = 0 }}}
{{{ x[4]/2 = 1/2 }}}
{{{ x[4] = 1 }}}
So, after the 4th stop,
{{{ x[3] - (x[3]/2 + 1/2) = 1}}}
{{{ x[3]/2 - 1/2 = 1 }}}
{{{ x[3]/2 = 3/2 }}}
{{{ x[3] = 3 }}}
After the 3rd stop,
{{{ x[2] - (x[2]/2 + 1/2) = 3}}}
{{{ x[2]/2 - 1/2 = 3 }}}
{{{ x[2]/2 = 7/2 }}}
{{{ x[2] = 7 }}}
After the 2nd stop,
{{{  x[1] - (x[1]/2 + 1/2) = 7 }}}
{{{ x[1]/2 - 1/2 = 7 }}}
{{{ x[1]/2 = 15/2 }}}
{{{ x[1] = 15 }}}
After the 1st stop,
{{{ x[0] - (x[0]/2 + 1/2) = 15 }}}
{{{ x[0] /2 - 1/2 = 15 }}}
{{{ x[0]/2 = 31/2 }}}
{{{ x[0] = 31 }}}
She started with 31 eggs
check answer:
31 - ( 15.5 + .5 ) = 31 - 16
31 - 16 = 15
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15 - ( 7.5 + .5 ) = 15 - 8
15 - 8 = 7
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7 - (3.5 + .5) = 7 - 4
7 - 4 = 3
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3 - (1.5 + .5) = 3 - 2
3 - 2 = 1
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1 - (.5 + .5) = 1 - 1
1 - 1 = 0
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OK