OK.
Let's say a member and a non member each visit the garden ' V ' times.
The non-member's cost for each visit is $6 .
The non member's cost for ' V ' visits is 6 V .
His total cost for the year is 6 V .
The member's cost for each visit is $3.
The member's cost for ' V ' visits is 3V .
His total cost for the year is 3V + the $24 to join.
We want to know what ' V ' is (how many times each one can visit)
if their total costs are the same.
So let's just write an equation that SAYS their costs are the same,
and see what ' V ' turns out to be.
Non-member's cost for the year = Member's cost for the year
6 V = 3 V + 24
Subtract 3V from each side: 3 V = 24
Divide each side by 3 : V = 8 .
-- If they both visit the garden 1, 2, 3, 4, 5, 6, or 7 times in the year,
the member will spend MORE than the non member.
-- If they both visit the garden 8 times in the year,
they'll both spend the same amount. ($48)
-- If they both visit the garden MORE than 8 times in the year,
the member will spend LESS than the non-member.
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That was the algebra way to do it.
Now here is the cheap, sleazy, logical, easy way to do it:
The non-member spends (6 - 3) = $3 MORE than the member for each visit ?
After how many visits does the $3 more each time add up to the $24 that
it cost the member to join for the year ?
$24 / $3 = 8 visits .