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At Sam’s Warehouse, a member pays $25 a year for membership, and buys at the regular store prices. A non-member does not pay the membership fee, but does pay an additional 5% above the store prices. Under what conditions would it make sense to buy a membership?

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It would make sense to buy a membership if you are planning on spending at least 500 dollars. At that point, the savings (5%) will equal the cost of the membership. 
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