Question 214180
Let {{{C}}} = the cost of the plans
Let {{{n}}} = number of guests
Plan A:
{{{C = 30n}}}
Plan B:
{{{C = 1300 + 20*(n - 25)}}}
I want all situations where Plan A costs more than Plan B
{{{30n > 1300 + 20*(n - 25)}}}
{{{30n > 1300 + 20n - 500}}}
{{{10n > 800}}}
{{{n > 80}}}
If the number of guests is greater than 80,
plan B costs less than Plan A
check answer:
Suppose there are 80 guests
Plan A:
{{{C = 30*80}}}
{{{C = 2400}}}
Plan B:
{{{C = 1300 + 20*(80 - 25)}}}
{{{C = 1300 + 20*55}}}
{{{C = 1300 + 1100}}}
{{{C = 2400}}} (break even point)
Suppose there are 81 guests:
Plan A:
{{{C = 30*81}}}
{{{C = 2430}}}
Plan B:
{{{C = 1300 + 20*(81 - 25)}}}
{{{C = 1300 + 20*56}}}
{{{C = 1300 + 1120}}}
{{{C = 2420}}} ($10 cheaper)
OK