Answer :
Final answer:
In this mathematical problem of profit calculation, the grocer purchased 120 pounds of bananas to achieve a $10 profit, by buying at $0.50 per 3 pounds and selling at $1.00 per 4 pounds.
Explanation:
The subject of this question is a basic mathematical problem dealing with profit calculation. Let's denote the quantity of bananas the grocer purchased by 'x' pounds. Since the grocer bought the bananas at a price of $0.50 per 3 pounds, the total cost of the bananas is ($0.50/3)*x. He sold the bananas at a price of $1.00 per 4 pounds, so the total revenue from selling the bananas is ($1.00/4)*x.
Since profit is defined as revenue minus cost, we set up the following equation to represent the grocer's profits: ($1.00/4)*x - ($0.50/3)*x = $10. By solving this equation algebraically, we can find the quantity of bananas the grocer purchased:
- Multiply the equation through by 12 to remove the denominators, resulting in 3x - 2x = 120.
- Simplifying gives x = 120 pounds, meaning the grocer purchased 120 pounds of bananas to achieve a profit of $10.
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Answer:
$10.00/($1.00/4 - $0.50/3) =
$10.00/(($3.00 - $2.00)/12) =
$10.00/($1.00/12) =
$10.00(12/$1.00) =
120 pounds of bananas
