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How do you translate “The sum of twice a number n and 20” into an algebraic statement?

Last updated date: 20th Jun 2024
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Hint: The skill of converting verbal statements/ algebraic expressions into equations requires an understanding of the words that are commonly used to represent mathematical operations. For example the common words used for “+” operator are “add”, “increased” etc. Unlike equations, algebraic expressions do not contain an “=” sign.

Complete step by step answer:
Here the statement is “the sum of twice a number n and 20”.
As we can clearly see the keywords used here are, “sum”, “twice” and “number n”.
The word “sum” immediately gives us the hint that we are going to add here, since it is addition we need two terms.
The two quantities are: “twice a number n” and the number 20.
The statement “twice a number n” means the number n is doubled or multiplied by 2
That is 2n.
Hence the two number to be added are 2n and 20
When we add the variable 2n and 20, we have 2n + 20. It is also okay to write your answer as 20 + 2n because addition is commutative, that is, switching the order of addition doesn’t change its sum.

Hence our final answer for “The sum of twice a number n and 20” is 2n+20.

Note: Algebraic expressions can be quite confusing sometimes, try to identify the keywords in the expression and then proceed into solving the expression. Sometimes the variables are not defined in the expression, it does not mean the variable does not exist in the final answer, in such cases we need to assume the variables and then mention it while giving our final answer. Keywords such as “a number”, “increased by some amount” etc means we need to assume a variable.