High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ 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)

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].