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Does buying more to get free delivery actually save money?

Imagine a $38 basket with free delivery starting at $40. Adding a $4 notebook takes your total to $42.

If delivery would have cost $6, your original order was $44. Adding the notebook saves $2.

If delivery was only $3, your original order was $41. Now the notebook costs you an extra dollar. The delivery fee changes which option is cheaper.

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