A store offers a "Buy 5 Get 2a free" scheme along with a trade discount of 10%. If the effective discount given to the customer is 50%, what is the value of a?
2
In a "Buy 5 Get 2a free" scheme the customer pays for 5 items and receives 5 + 2a items. With a further trade discount of 10%, the customer pays 90% of the price of 5 items.
Effective discount 50% means the amount paid is 50% of the marked price of all items received: \(0.9 \times 5 = 0.5 \times (5 + 2a)\).
So 4.5 = 2.5 + a, giving a = 2.
Check: with a = 2 the customer gets 5 + 4 = 9 items and pays 0.9 × 5 = 4.5 items' price; 4.5 ÷ 9 = 0.5, so the customer pays half and the effective discount is 50%.
Hence, 2.
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