Question
A shop marks a camera up by 50% over its wholesale cost, then advertises 20% off that marked price. A customer pays the discounted merchandise price plus a $12 delivery charge.
After a return-related complaint, the shop refunds 25% of what the customer paid for the merchandise, and separately refunds the entire $12 delivery charge. The customer has now paid a net $108 after both refunds. What was the shop's original wholesale cost of the camera?
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Hint 1
The shipping charge ultimately contributes nothing to the customer's net payment. Work backwards only through the adjustments to merchandise.
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Solution
Let C be the wholesale cost. The marked price is \(1.50C\). After the 20% sale reduction, the merchandise paid amount is \(0.80(1.50C)=1.20C\). The later refund is 25% of this amount, so the customer ultimately retains a charge of \(0.75(1.20C)=0.90C\) for the camera. The $12 delivery payment and the $12 delivery refund cancel exactly. The observed net payment therefore satisfies \(0.90C=108\), giving \(C=\$120\).
Forward-check: A $120 camera is marked at $180 and sold at $144. Adding $12 shipping produces an initial charge of $156. The shop subsequently returns $36 for merchandise and $12 for delivery, a $48 total refund. The final net payment is \(\$156-\$48=\$108\). The 25% refund applies to the discounted merchandise payment, not to the original wholesale cost or the total including shipping.
Assumptions
All percentages apply exactly as stated and there are no taxes or additional fees.
The delivery fee is charged and fully refunded independently of the merchandise refund.
The $108 amount is the customer’s final net cash outlay.
Final Answer
$120 wholesale cost.