Answer :
- Translates '8 times a number $x$' to $8x$.
- Adds 3 to represent '3 more than', resulting in $8x + 3$.
- Sets the expression equal to 83, forming the equation $8x + 3 = 83$.
- Identifies the correct equation as $\boxed{8x + 3 = 83}$.
### Explanation
1. Problem Analysis
Let's analyze the problem. The problem states that '3 more than 8 times a number $x$ is equal to 83'. We need to translate this statement into an algebraic equation and choose the correct option.
2. Translating to an Equation
'8 times a number $x$' can be written as $8x$. '3 more than' means we add 3 to this expression, so we have $8x + 3$. The problem states that this is equal to 83, so the equation is $8x + 3 = 83$.
3. Comparing with Options
Now, let's compare our equation $8x + 3 = 83$ with the given options:
A) $(3)(8)x = 83$ which simplifies to $24x = 83$
B) $8x = 83 + 3$ which simplifies to $8x = 86$
C) $3x + 8 = 83$
D) $8x + 3 = 83$
Option D matches our equation.
4. Final Answer
Therefore, the correct equation that represents the given situation is $8x + 3 = 83$.
### Examples
Understanding how to translate word problems into algebraic equations is a fundamental skill in mathematics. For example, if you are trying to calculate the total cost of items you are buying, where each item has a fixed price and there is a fixed shipping fee, you can use a similar equation. If each item costs $8 and the shipping fee is $3, and your total cost is $83, you can use the equation $8x + 3 = 83$ to find out how many items you bought.
- Adds 3 to represent '3 more than', resulting in $8x + 3$.
- Sets the expression equal to 83, forming the equation $8x + 3 = 83$.
- Identifies the correct equation as $\boxed{8x + 3 = 83}$.
### Explanation
1. Problem Analysis
Let's analyze the problem. The problem states that '3 more than 8 times a number $x$ is equal to 83'. We need to translate this statement into an algebraic equation and choose the correct option.
2. Translating to an Equation
'8 times a number $x$' can be written as $8x$. '3 more than' means we add 3 to this expression, so we have $8x + 3$. The problem states that this is equal to 83, so the equation is $8x + 3 = 83$.
3. Comparing with Options
Now, let's compare our equation $8x + 3 = 83$ with the given options:
A) $(3)(8)x = 83$ which simplifies to $24x = 83$
B) $8x = 83 + 3$ which simplifies to $8x = 86$
C) $3x + 8 = 83$
D) $8x + 3 = 83$
Option D matches our equation.
4. Final Answer
Therefore, the correct equation that represents the given situation is $8x + 3 = 83$.
### Examples
Understanding how to translate word problems into algebraic equations is a fundamental skill in mathematics. For example, if you are trying to calculate the total cost of items you are buying, where each item has a fixed price and there is a fixed shipping fee, you can use a similar equation. If each item costs $8 and the shipping fee is $3, and your total cost is $83, you can use the equation $8x + 3 = 83$ to find out how many items you bought.
