Understanding the Percentage Problem
The question asks us to find the value of a variable 'k'. We are given a relationship involving percentages: "25% of k is 10 less than 1800% of 10". Let's break this down step by step.
Step 1: Calculate 1800% of 10
First, we need to determine the value of "1800% of 10". Percentage means "per hundred", so 1800% can be written as $\frac{1800}{100}$.
- Calculation: $\frac{1800}{100} \times 10$
- Simplify: $18 \times 10$
- Result: $180$
So, 1800% of 10 is 180.
Step 2: Calculate "10 less than 1800% of 10"
The phrase "10 less than 1800% of 10" means we need to subtract 10 from the value we found in Step 1.
- Calculation: $180 - 10$
- Result: $170$
Therefore, "10 less than 1800% of 10" equals 170.
Step 3: Set up the equation for 'k'
The problem states that "25% of k is 10 less than 1800% of 10". We already found that "10 less than 1800% of 10" is 170.
Now, let's represent "25% of k" mathematically. 25% is equal to $\frac{25}{100}$ or $0.25$. So, "25% of k" is $0.25k$.
Our equation becomes:
$$0.25k = 170$$
Step 4: Solve for 'k'
To find the value of 'k', we need to isolate it in the equation.
$$0.25k = 170$$
Divide both sides by 0.25:
$$k = \frac{170}{0.25}$$
Since $0.25 = \frac{1}{4}$, we can rewrite the division as multiplication:
$$k = 170 \times \frac{1}{0.25}$$
$$k = 170 \times 4$$
$$k = 680$$
Conclusion
By following the steps and setting up the correct algebraic equation based on the percentage relationships described, we find that the value of k is 680.
