12 more than 8.2 times a number n answer
The correct answer and explanation is:
Correct Answer:
The expression “12 more than 8.2 times a number n” is written as: 8.2n+128.2n + 12
Explanation (300 words):
In mathematics, phrases in words can be translated into algebraic expressions using specific keywords. Let’s break down the phrase “12 more than 8.2 times a number n” step by step:
- “a number n” – This means the unknown number is represented by the variable nn.
- “8.2 times a number n” – This tells us to multiply the number nn by 8.2, giving the expression 8.2n8.2n. This is the base of our calculation.
- “12 more than” – This phrase means we are adding 12 to something. In math, “more than” often signals addition, and the number that follows (“12”) is added after the base. For example, “5 more than x” is written as x+5x + 5, not 5+x5 + x, although the result is the same in basic addition. But the order tells us which part is the base.
So when you say “12 more than 8.2 times n”, you are taking the base 8.2n, and adding 12 to it: Final expression: 8.2n+12\text{Final expression: } 8.2n + 12
Why This Is Useful:
This kind of word-to-algebra translation is essential in solving real-world problems in algebra, business, and science. For example, if someone earns $8.20 for every item they sell and also gets a $12 bonus, their total pay would be modeled as: Total Pay=8.2n+12\text{Total Pay} = 8.2n + 12
Where nn is the number of items sold.
Understanding how to build expressions like this prepares you for creating equations and solving for unknowns in a variety of contexts.