a. Let's break down the information given:
The trader bought m pineapples for $480.00.
15% of the pineapples were rotten.
She sold one pineapple for $0.59 more than the cost of the pineapple.
To find the cost of each pineapple in terms of m, we need to divide the total cost by the number of non-rotten pineapples. Since 15% of the pineapples were rotten, we have 85% of the pineapples that are not rotten.
Cost of each pineapple = $480.00 / (0.85m)
To find an expression for the total amount received from the sales, we need to consider the total number of pineapples sold and the selling price of each pineapple.
Let's assume she sold n pineapples. Since she sold each pineapple for $0.59 more than the cost, the selling price of each pineapple would be:
Selling price of each pineapple = Cost of each pineapple + $0.59
= $480.00 / (0.85m) + $0.59
The total amount received for the sales would be the selling price of each pineapple multiplied by the number of pineapples sold:
Total amount received for sales = n * (Cost of each pineapple + $0.59)
= n * ($480.00 / (0.85m) + $0.59)
b. If she made a profit of $84.00 from the sales:
i. To find the number of pineapples she originally bought, we need to solve the equation for the total amount received for sales:
Total amount received for sales = n * ($480.00 / (0.85m) + $0.59) = $480.00 + $84.00
ii. To find the cost price of one pineapple, we can substitute the number of pineapples she originally bought (m) into the expression for the cost of each pineapple:
Cost of each pineapple = $480.00 / (0.85m)
Once we solve the equation in part i, we can substitute the value of m into the expression for the cost of each pineapple to find the cost price.