Question 1083807
This is 2 interlocking circles giving you
3 distinct regions:
(1) Only like mango
(2) Like both mango and orange
(3) Only like orange
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They tell you that everything outside these
2 circles is {{{ 16 }}} children ( like none of them )
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Let {{{ C }}} = the total number of children
Area (1) Only like mango = {{{ ( 1/3)*C }}}
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{{{ 25 }}} do not like mango.
Let {{{ x }}} = (3) Only like orange
{{{ x + 16 = 25 }}}
{{{ x = 9 }}}
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{{{ (2/5)*C }}} = like orange
{{{ (2/5)*C - 9 }}} = area (2) Like both mango and orange
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I have specified the 3 areas and also everything outside ( {{{ 16 }}} children )
so, now I can say:
{{{ C = (1/3)*C + (2/5)*C - 9 + 9 + 16 }}}
{{{ C = (1/3)*C + (2/5)*C + 16 }}}
{{{ C = (5/15)*C + ( 6/15 )*C + 16 }}}
{{{ 15C = 5C + 6C + 240 }}}
{{{ 4C = 240 }}}
{{{ C = 60 }}}
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(2) Like both mango and orange = {{{ ( 2/5)*C - x }}}
{{{ (2/5)*C - x = (2/5)*60 - 9 }}}
{{{ (2/5)*C - x = 24 - 9 }}}
{{{ (2/5)*C - x = 15 }}}
So 15 children like both fruit
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check the answer:
{{{ (1/3)*C = (1/3)*60 }}}
{{{ (1/3)*C = 20 }}} = area (1)
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{{{ (2/5)*C - x = 15 }}} = area (2)
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{{{ x = 9 }}} = area (3)
and
{{{ 16 }}} = children who like neither fruit
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{{{ 20 + 15 + 9 + 16 = 60 }}}
{{{ 35 + 25 = 60 }}}
{{{ 60 = 60 }}}
OK