We are given the equation:

$25\% \text{ of } 400 + 35\% \text{ of } 1260 + 27\% \text{ of } 1800 = 1020 + x$

Step 1: Calculate each percentage

1. $25\% \text{ of } 400 = \frac{25}{100} \times 400 = 100$
2. $35\% \text{ of } 1260 = \frac{35}{100} \times 1260 = 441$
3. $27\% \text{ of } 1800 = \frac{27}{100} \times 1800 = 486$

Step 2: Add these values together

$100 + 441 + 486 = 1027$

Step 3: Set up the equation

$1027 = 1020 + x$

Step 4: Solve for $x$

$x = 1027 - 1020 = 7$

Thus, the value of $x$ is 7. Therefore, $x$ lies between 6 and 8.

Would you like more details, or do you have any questions?

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Here are 5 related questions:

1. What is 40% of 500?
2. How would the value of $x$ change if the percentages were increased by 5% each?
3. Can you solve for $x$ if $25\% \text{ of } 500 + 35\% \text{ of } 1300 + 27\% \text{ of } 1900 = 1120 + x$?
4. How do you find percentages of any given number?
5. What is the formula to calculate percentage change?

Tip: To solve percentage problems, always convert the percentage to a fraction or decimal before performing operations.