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------------------------------------------------ Use the equation [tex]\frac{1}{5} + s = \frac{32}{40}[/tex] to answer the questions.

Part A: Find possible values of [tex]s[/tex] using mathematical reasoning. Support your answer using the correct vocabulary. (2 points)

Part B: Solve for the variable [tex]s[/tex]. Show your work. (2 points)

We start with the equation
[tex]$$
\frac{1}{5} + s = \frac{32}{40}.
$$[/tex]

Step 1. Simplify the fraction on the right side. Notice that
[tex]$$
\frac{32}{40} = \frac{4}{5}.
$$[/tex]

Step 2. Rewrite the equation using the simplified fraction:
[tex]$$
\frac{1}{5} + s = \frac{4}{5}.
$$[/tex]

Step 3. Solve for [tex]$s$[/tex] by subtracting [tex]$\frac{1}{5}$[/tex] from both sides. This gives
[tex]$$
s = \frac{4}{5} - \frac{1}{5}.
$$[/tex]

Step 4. Subtract the fractions (since the denominators are the same) by subtracting the numerators:
[tex]$$
s = \frac{4-1}{5} = \frac{3}{5}.
$$[/tex]

Part A: Verification of the possible values
Since the equation has one equality sign, it requires that the sum of [tex]$\frac{1}{5}$[/tex] and [tex]$s$[/tex] must be exactly equal to [tex]$\frac{4}{5}$[/tex]. The only value of [tex]$s$[/tex] that satisfies this equality is [tex]$s = \frac{3}{5}$[/tex]. This means there is exactly one possible value for [tex]$s$[/tex] that makes the equation true.

Part B: Final answer
After isolating the variable [tex]$s$[/tex], we find that
[tex]$$
s = \frac{3}{5}.
$$[/tex]

Thus, the solution to the equation is [tex]$s = \frac{3}{5}$[/tex].