High School

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Part A: Solve for the value of \( s \).

To solve for \( s \), move \( \frac{1}{5} \) to the other side by changing its sign from positive to negative. Next, find the least common multiple of the two denominators, 40 and 5. Then proceed to solve:

\[
\frac{1}{5}s = \frac{32}{40}
\]

Subtract \( \frac{1}{5} \) from both sides:

\[
s = \frac{32}{40} - \frac{1}{5}
\]

Convert \( \frac{1}{5} \) to a denominator of 40:

\[
s = \frac{32}{40} - \frac{8}{40}
\]

Simplify:

\[
s = \frac{24}{40}
\]

Simplify further:

\[
s = \frac{3}{5}
\]

Choose the correct option:

A) \( s = \frac{3}{5} \)
B) \( s = \frac{5}{3} \)
C) \( s = \frac{4}{5} \)
D) \( s = \frac{5}{4} \)

Answer :

Final Answer:

In part a), we first isolate [tex]\( s \)[/tex] by moving [tex]\( \frac{1}{5}s \)[/tex] to the other side, resulting in [tex]\( s = -\frac{1}{5} \times \frac{1}{8} \)[/tex] , which simplifies to [tex]\( s = \frac{3}{5} \)[/tex] In part b), we apply the same procedure and find [tex]\( s = \frac{3}{5} \)[/tex] confirming the answer from part a). Therefore, option a)[tex]\( s = \frac{3}{5}[/tex] is correct.

Explanation:

a) To solve the equation [tex]\( \frac{1}{5}s = \frac{1}{8} \)[/tex] , the first step is to isolate [tex]\( s \)[/tex] . We achieve this by rearranging the equation, bringing [tex]\( \frac{1}{5}s \)[/tex] to the other side. This results in [tex]\( s = -\frac{1}{5} \times \frac{1}{8} \)[/tex]. Simplifying, we find [tex]\( s = \frac{3}{5} \)[/tex].

b) Given [tex]\( \frac{1}{5}s = \frac{32}{40} \)[/tex], we first find a common denominator, then subtract [tex]\( \frac{1}{5}s \)[/tex] from both sides. This yields [tex]\( s = \frac{3}{5} \)[/tex] as calculated in part (a). Therefore, option a) [tex]\( s = \frac{3}{5} \)[/tex] is the correct answer.

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