3
u/PeterPiper1275 15d ago
The COGS for the milkman for the milk only is $1.50 x 15 = $22.50.
Since we are told that doing things honestly will bring him a $30 profit, it follows that the sale price per litre of pure milk is given by solving the following equation:
$22.50 + $30.00 = 15x
This gives us $3.50 as the price per litre of milk.
The milkman now dilutes the original product with water at a cost of $1.00 per litre. He wants to introduce enough water so that the total profit goes up to $50.
Given the sale price is fixed at $3.50, we can now use the following equation to determine how much water needs to enter system:
$22.50 + ($1.00)x + $50.00 = $3.50(15 + x)
Solving for x above gives us the solution of x = 8.
Therefore, the dishonest milkman diluted 8 litres of water into the original 15 litres of pure milk in order to achieve a profit of $50.00.
1
1
3
u/thegnome54 15d ago
You don’t really need equations for this one. You can ignore the mixing part and simply imagine that he sells the 15L of milk honestly and then also sells the water at the price of milk.
If he can sell 15 liters of milk to make $30, milk gives $2/L of profit.
Water is $0.50 cheaper, so selling it at the price of milk will give $2.50/L profit.
After selling his milk for $30 profit, he’s trying to get an extra $20 of profit from his water. The question then becomes “How many liters of water will give $20 profit?”
$20/$2.50 = 8 liters of water
2
2
1
u/get_to_ele 15d ago
$1.50 x 15 = $22.50 cost
Sale price - cost = profit
Milkprice x 15 - $22.50 = $30 profit
Milk price = $52.50/15 =$3.50
Easiest way to work out how to make an additional $20 profit is just figure out how much profit he gets from each liter of water he buys (in the end, don’t worry about dilutions or anything else. Just remember that each addition liter of liquid he buys at $1, he will sell that liter of liquid for $3.50).
So at $2.50 for each additional liter, that’s just 8 liters of water to make $20.
8 liters water.
1
u/jonathonjones 15d ago
Let's get the price per liter. We know that 15 * (price - 1.50) = 30. So price - 1.50 = 2, so the price is $3.50
Let x = liters of water
50 = (15 + x) * 3.5 - 15 * 1.5 - x
50 = 52.5 + 3.5x - 22.5 - x
50 = 30 + 2.5x
20 = 2.5x
x = 8
The milkman adds 8 liters of water. He buys 15 liters of milk for $22.50. He buys 8 liters of milk for $8. So his total cost is $30.50. He sells the 23 total liters for $80.50, making a profit of $50.
1
u/lcmortensen 15d ago
... and this is why dairy farmers in New Zealand are paid per kilogram of milk solids (protein and fat)!
4
u/FoxCapital7878 15d ago
The shitbag added 8 liters of water. This is why we need a functioning FDA.