Paper pulp is sold on the basis that it contains 12% moisture; if the moisture exceeds this
value, the purchaser can deduct any charges for the excess moisture and also deduct for the
freight costs of the excess moisture. A shipment of pulp became wet and was received with
a moisture content of 22%. If the original price for the pulp was $40/ton of air-dry pulp and
if the freight is $1.00/100 lb shipped, what price should be paid per ton of pulp delivered?
Sounds like a math problem to me. The way I read it, there is an excess moisture content of 10% so the $40/ton is reduced by $4/ton to make it $36/ton. It cost $1.00/100 lb or $20.00/ton for shipping [$1.00 x (2000 lbs/100 lb)] and 10% of the $20.00 is $2.00/ton so 40-4-2 = $34.00/ton on the as received merchandise.
To calculate the price per ton of pulp delivered, we need to consider the excess moisture and freight costs.
First, let's calculate the excess moisture in the shipment:
Excess moisture = Moisture content - Allowed moisture content
Excess moisture = 22% - 12%
Excess moisture = 10%
Next, we need to calculate the weight of the excess moisture:
Weight of excess moisture = Excess moisture * Weight of shipment
Weight of excess moisture = 10% * Weight of shipment
Since the weight of the shipment is not given, we cannot calculate the exact weight of excess moisture. However, we can proceed with the calculation by assuming a weight value.
Let's assume the weight of the shipment is 1000 pounds. Therefore, the weight of excess moisture would be:
Weight of excess moisture = 10% * 1000 pounds
Weight of excess moisture = 0.10 * 1000 pounds
Weight of excess moisture = 100 pounds
Now, let's calculate the cost of the excess moisture:
Cost of excess moisture = Freight cost per 100 pounds * Weight of excess moisture / 100
Cost of excess moisture = $1.00 * 100 pounds / 100
Cost of excess moisture = $1.00
Next, we need to calculate the cost of the air-dry pulp:
Cost of air-dry pulp = Original price - Cost of excess moisture
Cost of air-dry pulp = $40.00 - $1.00
Cost of air-dry pulp = $39.00
Finally, let's calculate the cost per ton of pulp delivered:
Cost per ton of pulp delivered = Cost of air-dry pulp / (1 - Moisture content / 100)
Cost per ton of pulp delivered = $39.00 / (1 - 22% / 100)
Cost per ton of pulp delivered = $39.00 / (1 - 0.22)
Cost per ton of pulp delivered = $39.00 / 0.78
Cost per ton of pulp delivered = $50.00
Therefore, the price to be paid per ton of pulp delivered is $50.00.
To find the price that should be paid per ton of pulp delivered, we need to calculate the deductions for the excess moisture and the freight costs for the excess moisture.
Let's break down the steps:
Step 1: Calculate the moisture deduction:
- The pulp is sold on the basis that it contains 12% moisture, so any moisture content above that will result in a deduction.
- The moisture content of the shipment is 22%, which means there is an excess of 22% - 12% = 10% moisture.
- The deduction for the excess moisture is calculated as a percentage of the original price.
Step 2: Calculate the freight deduction:
- The freight costs for the excess moisture are calculated based on the weight of the excess moisture.
- The weight of the excess moisture is determined by multiplying the moisture content (10%) by the weight of the shipment (let's assume it's X tons).
Step 3: Calculate the total deductions:
- The total deductions will be the sum of the moisture deduction and the freight deduction.
Step 4: Calculate the final price per ton:
- The final price per ton is calculated by subtracting the total deductions from the original price and dividing it by the weight of the air-dry pulp.
Now, let's calculate each step:
Step 1: Calculate the moisture deduction:
- The moisture deduction is 10% of the original price ($40/ton).
- 10% of $40 is (10/100) x $40 = $4.
Step 2: Calculate the freight deduction:
- The weight of the excess moisture is 10% of the weight of the shipment (X tons) because the excess moisture is 10% of the total moisture content.
- The weight of the excess moisture is (10/100) x X = 0.1X tons.
- The freight costs for the excess moisture are $1.00 per 100 lb, which is equivalent to $1.00 per (1/20) ton (since 1 ton = 2000 lb).
- Therefore, the freight deduction is $1.00 x (0.1X) x (20/1) = $2X.
Step 3: Calculate the total deductions:
- The total deductions are the sum of the moisture deduction and the freight deduction.
- Total deductions = $4 + $2X.
Step 4: Calculate the final price per ton:
- The final price per ton is calculated by subtracting the total deductions from the original price ($40) and dividing it by the weight of the air-dry pulp (X tons).
- Final price per ton = ($40 - ($4 + $2X)) / X.
So, the price per ton of pulp delivered should be ($40 - ($4 + $2X)) / X.