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Select the correct answer.

Given the formula [tex]\( A = P(1 + rt) \)[/tex] with [tex]\( A = 27 \)[/tex] and [tex]\( t = 3 \)[/tex], solve for [tex]\( r \)[/tex].

A. [tex]\( r = \frac{27 - 1}{3P} \)[/tex]

B. [tex]\( r = \frac{27 - P}{3} \)[/tex]

C. [tex]\( r = \frac{27 - P}{3P} \)[/tex]

D. [tex]\( r = \frac{26}{3} \)[/tex]



Answer :

GinnyAnswer
To solve for [tex]\( r \)[/tex] given the formula [tex]\( A = P(1 + r t) \)[/tex] with [tex]\( A = 27 \)[/tex] and [tex]\( t = 3 \)[/tex], let's break down the problem step by step.

First, we substitute the given values into the formula:

[tex]\[ 27 = P(1 + r \cdot 3) \][/tex]

Now, solve for [tex]\( r \)[/tex]:

1. Start with the original equation:

[tex]\[ 27 = P(1 + 3r) \][/tex]

2. Isolate the term containing [tex]\( r \)[/tex]:

[tex]\[ \frac{27}{P} = 1 + 3r \][/tex]

3. Subtract 1 from both sides:

[tex]\[ \frac{27}{P} - 1 = 3r \][/tex]

4. To simplify, represent [tex]\( \frac{27}{P} - 1 \)[/tex] as a single fraction:

[tex]\[ \frac{27 - P}{P} = 3r \][/tex]

5. Solve for [tex]\( r \)[/tex] by dividing both sides by 3:

[tex]\[ r = \frac{27 - P}{3P} \][/tex]

After working through these steps, we reach the expression for [tex]\( r \)[/tex]:

[tex]\[ r = \frac{27 - P}{3P} \][/tex]

Now, compare this with the given options:

A. [tex]\( r = \frac{27 - 1}{3P} \)[/tex]

B. [tex]\( r = \frac{27 - P}{3} \)[/tex]

C. [tex]\( r = \frac{27 - P}{3P} \)[/tex]

D. [tex]\( r = \frac{26}{3} \)[/tex]

The correct answer is clearly Option C:

[tex]\[ \boxed{r = \frac{27 - P}{3P}} \][/tex]

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