Question 1070580
Let {{{ x }}} = total members of the red hat society
{{{ .8x }}} = those over 65 yrs old
{{{ .8*( .8x ) = .64x }}} = those over 75 yrs old 
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given:
{{{ .8x - .64x = 240 }}}
{{{ .16x = 240 }}}
{{{ x = 1500 }}}
and
{{{ .64x = .64*1500 }}}
{{{ .64x = 960 }}}
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960 members are over 75
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check:
Those under 65:
{{{ x - .8x = .2x }}}
{{{ .2x = .2*1500 }}}
{{{ .2x = 300 }}}
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Those 65 - 75:
{{{ .8x - .64x = .16x }}}
{{{ .16x = .16*1500 }}}
{{{ .16x = 240 }}}
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Those over 75:
{{{ .8*( .8x ) = .64x }}}
{{{ .64x = .64*1500 }}}
{{{ .64x = 960 }}}
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{{{ 300 + 240 + 960 = 1500 }}}
OK