MHB Did John Profit from His Apple Sales Strategy?

[maxkor]

John bought a certain amount of apples packed in boxes containing after three kilograms of fruit, paying for each 10 dollars . Then sold all the apples purchased at a price 9 dollars per bag, but each of the bags contains only 2.35 kilograms of fruit. How many kilograms of apples bought John, if the sale of all the apples was (after deducting the cost of purchase) 1260 dollars?

 

[soroban]

Hello, maxkor!

John bought apples packed in boxes containing 3 kg of fruit, paying \$10 per box.
Then he sold the apples at \$9 per bag; each bag contains 2.35 kg of fruit.
How many kg of apples did John buy, if the profit was \$1260 dollars?

Let b = number of boxes of apples that John bought.

His cost was 10b dollars.

He bought $3b$ kg of apples.

He divided them into $\frac{3b}{235}$ bags and sold them at \$9 each.
His revenue is: $9\left(\frac{3b}{2.3}\right) \,=\,\frac{27b}{2.35}$ dollars.

His profit is \$1260.
There is our equation! $\;\;\frac{27b}{2.35} - 10b \:=1260 $

Answer: \:b \:=\: 846\text{ boxes} \:=\:2538\text{ kg apples}