Identify the equation for the relationship below:
Three of an unknown number plus two more makes a total of 50.
A. [tex]$3 x=50+2$[/tex]
B. [tex]$3 x+2=50$[/tex]
C. [tex]$(3+2) x=50$[/tex]
D. [tex]$3+x+2=50$[/tex]
Answer (2)
Represent the unknown number with the variable x .
Translate "Three of an unknown number plus two more makes a total of 50" into an algebraic expression.
Form the equation 3 x + 2 = 50 .
The correct equation that represents the relationship is 3 x + 2 = 50 .
Explanation
Understanding the Problem Let's break down the problem step by step to form the correct equation.
Translating the Words The problem states: "Three of an unknown number plus two more makes a total of 50." We need to translate this into an algebraic equation.
Breaking Down the Sentence Let's use 'x' to represent the unknown number.
"Three of an unknown number" translates to 3 x .
"plus two more" translates to + 2 .
"makes a total of 50" translates to = 50 .
Forming the Equation Combining these parts, the equation becomes 3 x + 2 = 50 .
Comparing with Options Now, let's compare this equation with the given options:
3 x = 50 + 2 is incorrect because it implies three times the number equals 52, not that adding 2 to three times the number equals 50.
3 x + 2 = 50 is the equation we derived, so it's correct.
( 3 + 2 ) x = 50 simplifies to 5 x = 50 , which means five times the number equals 50, not three times the number plus 2.
3 + x + 2 = 50 simplifies to x + 5 = 50 , which means the number plus 5 equals 50, not three times the number plus 2.
Final Answer Therefore, the correct equation is 3 x + 2 = 50 .
Examples
Imagine you're trying to figure out how many apples you can buy. Each apple costs $3, and you also have to pay a $2 entrance fee to the orchard. If you have $50 in total, the equation 3 x + 2 = 50 helps you determine the maximum number of apples (x) you can buy. This type of problem is a simple example of how linear equations are used in everyday budgeting and purchasing decisions.
The correct equation for the relationship described in the problem is 3 x + 2 = 50 . This is based on translating the English statement into an algebraic expression. The corresponding multiple choice option is B.
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