A merchant purchases two lots of shoes. One lot is purchased for $32 per pair, and the second lot is purchased for $40 per pair. There are 50 pairs in the first lot. How many pairs are in the second lot if he sold them all at $60 per pair and made a gain of $2800 on the entire transaction?

The subject of the question is to determine how many pairs of shoes were in the second lot of a business transaction. This involves understanding the concept of profit calculation and unit cost estimation .
Let's denote the number of pairs in the second lot as x . The total cost for the first lot is 50 pairs × $32/pair = $1600. The total cost for the second lot is x pairs × $40/pair = $40x. The selling price for all the pairs is ($60/pair) × (50 + x ). The merchant made a gain (profit) of $2800 on the entire transaction. The equation for the total profit is:
Total Revenue - Total Cost = Profit
(60 × (50 + x )) - (1600 + 40x) = 2800
Now we solve for x :
3000 + 60x - 1600 - 40x = 2800
20x + 1400 = 2800
20x = 1400
x = 70
There were 70 pairs in the second lot.

Answered by MonteBlue | 2024-06-18

The merchant purchased 70 pairs of shoes in the second lot. After calculating the costs and profits, the total number of pairs in the second lot was determined to be 70. The problem involved setting up equations for total cost and revenue based on selling prices and profit from the sales.
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Answered by MonteBlue | 2024-10-12