How many total pounds are required for 18,000 CCY of material considering a shrinkage factor of 10%?

Understand the Problem

The question is asking for the total pounds of material needed after accounting for a shrinkage factor of 10% on 18,000 CCY (Cubic Yards) of material. To solve this, we will first determine the amount before shrinkage and then apply the shrinkage factor to get the final amount.

Answer

$16,200$ cubic yards

Steps to Solve

Calculate the volume before shrinkage

Start with the total volume of material which is provided as 18,000 cubic yards.

Determine the shrinkage factor

Shrinkage is given as 10%, which can be expressed as a decimal for calculation:

$$ 10% = 0.10 $$

Calculate the volume after applying shrinkage

To find the final volume after shrinkage, we can multiply the original volume by the shrinkage factor and then subtract that from the original amount.

The equation will be:

$$ \text{Final Volume} = \text{Original Volume} - (\text{Original Volume} \times \text{Shrinkage}) $$

Putting in the values:

$$ \text{Final Volume} = 18,000 - (18,000 \times 0.10) $$

Perform the calculations

First calculate the amount lost to shrinkage:

$$ 18,000 \times 0.10 = 1,800 $$

Now, subtract this value from the original volume:

$$ \text{Final Volume} = 18,000 - 1,800 = 16,200 $$

The total pounds of material needed after accounting for shrinkage is $16,200$ cubic yards.

More Information

When working with quantities that experience shrinkage, it's important to always account for that percentage properly to avoid underestimating the material needed. Understanding how to apply percentage reductions is key in many real-world applications, including construction and manufacturing.

Tips

Forgetting to convert percentage shrinkage into a decimal format before using it in calculations. Always ensure to convert percentages by dividing by 100.
Not subtracting the shrinkage from the original volume; it's essential to perform that subtraction correctly to find the final amount.

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