A dealer bought some grapefruits for $1.04. After throwing away 4 bad ones, he sold the other ones at 6 cents apiece more than he had paid for them and made a profit of $0.22. How many did he buy?
(x-4)(104/x+6) = 104+22
x = 13
So, he bought 13 at 8 cents, and sold 9 at 14 cents
can you show how the equation would be solved?
(x-4)(104/x+6) = 126
104 + 6x - 416/x -24 - 126 = 0
6x - 46 - 416/x = 0
times x
6x^2 - 23x - 416 = 0
3x^2 - 11x - 208 = 0
(x - 13)(3x + 16) = 0
x = 13 or x = -16/3, but x can't be negative, so
x = 13
To solve this problem, we need to determine the original number of grapefruits the dealer bought.
Let's assume the dealer bought 'x' grapefruits.
The cost of each grapefruit is $1.04, so the total cost of 'x' grapefruits is $1.04 * x.
After throwing away 4 bad grapefruits, the dealer has 'x' - 4 good grapefruits left.
The dealer sold the remaining grapefruits at a price that was 6 cents (or $0.06) higher than what he paid for each grapefruit. So the selling price per grapefruit is $1.04 + $0.06 = $1.10.
The profit made from selling the grapefruits is $0.22.
Profit = Selling price - Cost price
Using this formula, we can calculate the cost price of the grapefruits:
$0.22 = (x - 4) * $1.10 - $1.04 * x
Simplifying the equation:
$0.22 = $1.10x - $4.40 - $1.04x
$0.22 = $0.06x - $4.40
Adding $4.40 to both sides:
$4.62 = $0.06x
Dividing both sides by $0.06:
x = 4.62 / 0.06
x ≈ 77
Therefore, the dealer bought approximately 77 grapefruits.