Question 957059
Let {{{ C }}} = the cost of the plan
Let {{{ n }}} = number of trips to water park
Plan a:
{{{ C = 8n + 147 }}}
Plan b:
{{{ C = 21n + 52 }}}
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Make the costs of (a) and (b) equal
{{{ 8n + 147 = 21n + 52 }}}
{{{ 13n = 95 }}}
{{{ n = 7.3077 }}}
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A person cannot make a fraction of a visit,
and {{{ 7 }}} doesn't make the costs equal, 
so {{{ 8 }}} visits must be made
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check:
{{{ C = 8n + 147 }}}
{{{ C = 8*7.3077 + 147 }}}
{{{ C = 205.4615 }}}
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{{{ C = 21n + 52 }}}
{{{ C = 21*7.3077 + 52 }}}
{{{ C = 205.4617 }}}
close enough