The average transaction made with cash or a gift card is $90.
What is Transaction?
A financial transaction is an agreement, or communication, between a buyer and seller to exchange goods, services, or assets for payment.
The expected value of store card transactions will be the product of their average value ($58) and their probability of occurrence (48%).
... $58 × 0.48 = $27.84
Transactions are either "store card" or "without a store card", so the probability of a transaction being made without a store card is
... 1 - 0.48 = 0.52
Using the same computation as for store card expected value, the expected value of transactions made without a store card is
... $74 × 0.52 = $38.48
The expected value of the store's transactions is the sum of the expected values of the different ways transactions can be made:
... $27.84 +38.48 = $66.32
The average value of transactions made without a store card is the weighted average of those made with another card and those made with cash or a gift card.
Using c to represent the latter, this weighted sum is ...
... 74 = 0.80 × 70 + 0.20 × c
... 74 -56 = 0.20c . . . . .
... 18/0.2 = c
c = 90
Thus, the average transaction made with cash or a gift card is $90.
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