Question 1016442
The rates of consumption of meat is the same
in both cases, I will say the rate is
[ rate ] = [ kg of meat ] / [ number of lions x time period being fed ]
Now I can set the rates in both cases equal to eachother:
Let {{{ n }}} = number of days that 200 kg of meat will feed 14 lions
{{{ 500 / ( 20*7 ) = 200 / ( 14*n ) }}} 
Divide both sides by {{{ 100 }}}
{{{ 5 / 140 = 2 / 14n }}}
Multiply both sides by {{{ 140n }}}
{{{ 5n = 20 }}}
{{{ n = 4 }}}
200 kg of meat will feed 14 lions for 4 days
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check:
{{{ 5 / 140 = 2 / 14n }}}
{{{ 5 / 140 = 2 / 14*4 }}}
{{{ 1 / 28 = 2 / 56 }}}
{{{ 1/28 = 1 / 28 }}}
OK