let the number of books she can buy be x
x ≤ 150/4
x ≤ 37.5 books
but x must be a whole number, so
x ≤ 37
if she buys 37 books, cost = 4(37) = 148, which is within her limit
if she buys 38 books, cost = 4(38) = 152 , which goes over her limit of 150
so x ≤ 37
single use: cost = 37.50n, where n is the number of uses
member use: cost = 285
we want 37.5n ≤ 285
divide by 37.5
n ≤ 285/37.5
n ≤ 7.6
but we can't have a partial visit, so consider
n = 7 or n = 8
Well, with the single use plan,
7 visits would cost 7(37.5) or $262.50 which is < 285
8 visits would cost 8(37.5) or $300 which is > 285
So for 8 or more visits, the membership plan would be best, for 7 or less the single use plan would be better.
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