Let's break down the expression step by step:

The expression is:

\[
100 + (90 + 15) \times 10 - 200
\]

### Step 1: Simplify the parentheses
First, simplify inside the parentheses:

\[
90 + 15 = 105
\]

Now the expression becomes:

\[
100 + 105 \times 10 - 200
\]

### Step 2: Perform the multiplication
Now multiply \( 105 \times 10 \):

\[
105 \times 10 = 1050
\]

Now the expression is:

\[
100 + 1050 - 200
\]

### Step 3: Perform the addition and subtraction
First, add \( 100 + 1050 \):

\[
100 + 1050 = 1150
\]

Now subtract \( 200 \):

\[
1150 - 200 = 950
\]

So, the final result is:

\[
\boxed{950}
\]

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. What is the result of \( (150 + 25) \times 5 - 100 + 50 \)?
2. How would the expression change if there were division instead of multiplication in \( (90 + 15) \)?
3. Can you simplify \( 120 + (85 + 20) \times 4 - 300 \)?
4. How does order of operations affect the outcome in similar expressions?
5. What would happen if we inserted exponents into a similar expression?

**Tip:** Always remember to follow the order of operations: parentheses first, then multiplication/division, followed by addition/subtraction.

Learn how to solve the arithmetic expression 100 + (90 + 15) x 10 - 200 step by step. This problem demonstrates key mathematical concepts like the order of operations (PEMDAS) and basic arithmetic operations. Suitable for students in Grades 5-7.

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