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Answer :
- First, simplify inside the parenthesis: $13 + 140 \\div 20 = 20$.
- Then, perform the multiplications: $159 \\cdot 20 = 3180$, $159 \\cdot 7 = 1113$, and $27 \\cdot 41 = 1107$.
- Finally, add all the results: $3180 + 1113 + 1107 = 5400$.
- The final answer is $\boxed{5400}$.
### Explanation
1. Understanding the Expression
We are given the expression $159(13+140 \\div 20)+159 \\cdot 7+27 \\cdot 41$ and we need to evaluate it. To do this, we will follow the order of operations (PEMDAS/BODMAS).
2. Simplifying Parentheses
First, we simplify the expression inside the parenthesis: $13 + 140 \\div 20 = 13 + 7 = 20$.
3. Multiplication
Next, we multiply the result by 159: $159 \\cdot 20 = 3180$.
4. Multiplication
Now, we calculate $159 \\cdot 7 = 1113$.
5. Multiplication
Then, we calculate $27 \\cdot 41 = 1107$.
6. Addition
Finally, we add the results from the previous steps: $3180 + 1113 + 1107 = 5400$.
### Examples
This type of calculation is useful in everyday situations such as calculating the total cost of items with discounts and taxes, or determining the total number of resources needed for a project. For example, if you are buying 159 items that cost $20 each, plus an additional 159 items that cost $7 each, and 27 items that cost $41 each, the expression helps you find the total cost.
- Then, perform the multiplications: $159 \\cdot 20 = 3180$, $159 \\cdot 7 = 1113$, and $27 \\cdot 41 = 1107$.
- Finally, add all the results: $3180 + 1113 + 1107 = 5400$.
- The final answer is $\boxed{5400}$.
### Explanation
1. Understanding the Expression
We are given the expression $159(13+140 \\div 20)+159 \\cdot 7+27 \\cdot 41$ and we need to evaluate it. To do this, we will follow the order of operations (PEMDAS/BODMAS).
2. Simplifying Parentheses
First, we simplify the expression inside the parenthesis: $13 + 140 \\div 20 = 13 + 7 = 20$.
3. Multiplication
Next, we multiply the result by 159: $159 \\cdot 20 = 3180$.
4. Multiplication
Now, we calculate $159 \\cdot 7 = 1113$.
5. Multiplication
Then, we calculate $27 \\cdot 41 = 1107$.
6. Addition
Finally, we add the results from the previous steps: $3180 + 1113 + 1107 = 5400$.
### Examples
This type of calculation is useful in everyday situations such as calculating the total cost of items with discounts and taxes, or determining the total number of resources needed for a project. For example, if you are buying 159 items that cost $20 each, plus an additional 159 items that cost $7 each, and 27 items that cost $41 each, the expression helps you find the total cost.
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