Final answer:
The question involves calculating the selling price given a cost price and profit or loss percentage, and vice versa. Students apply formulas to adjust the cost price by the given percentage to find the selling price, or adjust the selling price by the given percentage to find the cost price.
Step-by-step explanation:
The student is working on problems involving percentages, cost price (CP), selling price (SP), profit, and loss, which are fundamental concepts in high school mathematics, particularly within the subject of algebra or business math.
To find the selling price when given the cost price and the profit percentage, you use the formula SP = CP + (Profit% of CP). For example, with a CP of $5100 and a profit of 30%, the SP is calculated as $5100 + (30% of $5100) = $5100 + $1530 = $6630. Similarly, to find the selling price with a loss percentage, subtract the loss from the cost price, SP = CP - (Loss% of CP). Therefore, with a CP of $1700 and a loss of 10%, the SP is $1700 - (10% of $1700) = $1700 - $170 = $1530.
Conversely, to find the cost price from a selling price and profit or loss percentage, use the formula CP = SP / (1 + Profit%) for profit, or CP = SP / (1 - Loss%) for loss. For instance, with an SP of $180 and a loss of 25%, the CP is $180 / (1 - 25%) = $180 / 0.75 = $240. With an SP of $875 and a profit of 75%, the CP is $875 / (1 + 75%) = $875 / 1.75 = $500.
To solve the specific problem of a CP of $400 and a profit of 12 1/2%, you would calculate the SP as follows: $400 + (12.5% of $400) = $400 + $50 = $450.