What is the algebraic expression for "Twenty more than a number divided by three"?
A. [tex]$20+\frac{x}{3}$[/tex]
B. [tex]$\frac{x-20}{3}$[/tex]
C. [tex]$\frac{20-x}{3}$[/tex]
D. [tex]$\frac{x+20}{3}$[/tex]
Answer (2)
Represent the number as x .
Divide the number by three: 3 x .
Add twenty to the result: 20 + 3 x .
The algebraic expression is 20 + 3 x .
Explanation
Understanding the Expression Let's break down the phrase "Twenty more than a number divided by three" step by step to translate it into an algebraic expression.
Representing the Number First, we represent "a number" with the variable x .
Dividing by Three Next, we translate "divided by three" into a mathematical operation: 3 x . This means we are taking the number x and dividing it by 3.
Adding Twenty Finally, "Twenty more than" means we need to add 20 to the result of the division. So, we add 20 to 3 x , which gives us 20 + 3 x .
Final Expression Therefore, the algebraic expression for "Twenty more than a number divided by three" is 20 + 3 x .
Examples
Imagine you're splitting a bill with friends. If the total bill is 'x' dollars and you divide it equally among three friends, each person pays 3 x dollars. Now, if you add a $20 tip to the total bill before splitting it, the expression 20 + 3 x represents how much each person would pay. This kind of expression helps in everyday calculations involving division and addition.
The algebraic expression for "Twenty more than a number divided by three" is 20 + 3 x . This is represented by option A. Thus, the answer is option A: 20 + 3 x .
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