Which value of [tex]$f$[/tex] makes [tex]$3 f+5=32$[/tex] a true statement?
A. [tex]$f=6$[/tex]
B. [tex]$f=8$[/tex]
C. [tex]$f=9$[/tex]
D. [tex]$f=12$[/tex]
Answer (2)
Subtract 5 from both sides of the equation: 3 f = 32 − 5 = 27 .
Divide both sides by 3: f = 3 27 .
Simplify to find the value of f .
The value of f that satisfies the equation is 9 .
Explanation
Understanding the problem We are given the equation 3 f + 5 = 32 and we need to find the value of f that makes this equation true.
Isolating the term with f First, we subtract 5 from both sides of the equation to isolate the term with f :
3 f + 5 − 5 = 32 − 5
Simplifying the equation This simplifies to: 3 f = 27
Solving for f Next, we divide both sides of the equation by 3 to solve for f :
3 3 f = 3 27
Finding the value of f This simplifies to: f = 9 So, the value of f that makes the equation true is 9.
Examples
Imagine you are buying concert tickets. Each ticket costs $3, and there's a $5 service fee for the entire order. If your total bill is $32, this problem helps you calculate how many tickets you bought. The equation 3 f + 5 = 32 models this situation, where f is the number of tickets. Solving for f tells you exactly how many friends you can bring along!
The value of f that satisfies the equation 3 f + 5 = 32 is 9 . Therefore, the correct answer is option C. f = 9 .
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