Question 1034775
(a)
{{{ ( 35 + x ) / ( 50 + x ) = .8 }}}
{{{ 35 + x = .8*( 50 + x ) }}}
{{{ 35 + x = 40 + .8x }}}
{{{ .2x = 5 }}}
{{{ x = 25 }}}
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If she makes 25 more free throws in a row,
her % will be 80%
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check:
{{{ ( 35 + 25 ) / ( 50 + 25 ) = .8 }}}
{{{ 60 / 75 = .8 }}}
{{{ .8 = .8 }}}
OK
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(b)
{{{ 35 / ( 50 + x ) = .6 }}}
{{{ 35 = .6*( 50 + x ) }}}
{{{ 35 = 30 + .6x }}}
{{{ .6x = 5 }}}
{{{ x = 8.333 }}}
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If she misses 8 in a row, her % is:
{{{ 35 / ( 50 + 8 ) = 35/58 }}}
{{{ (35/58)*100 = 60.34 }}}
60.34%
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If she misses 9 in a row, her % is:
{{{ 35 / ( 50 + 9 ) = 35/59 }}}
{{{ (35/59)*100 = 59.32 }}}
59.32%
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The greatest number of misses before her
% drops below 60% is 8