Answer :
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].
[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].