College

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. Show your work. (2 points)

Answer :

Let's solve the equation [tex]\(\frac{1}{5} + s = \frac{32}{40}\)[/tex] and find the value of [tex]\(s\)[/tex].

### Part A: Find possible values of [tex]\(s\)[/tex].

To solve for [tex]\(s\)[/tex], we need to isolate it on one side of the equation. We start with:

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

First, convert [tex]\(\frac{1}{5}\)[/tex] to a fraction with a denominator of 40, to match [tex]\(\frac{32}{40}\)[/tex].

[tex]\[
\frac{1}{5} = \frac{8}{40}
\][/tex]

Now we have:

[tex]\[
\frac{8}{40} + s = \frac{32}{40}
\][/tex]

### Part B: Solve for [tex]\(s\)[/tex].

Subtract [tex]\(\frac{8}{40}\)[/tex] from both sides to solve for [tex]\(s\)[/tex]:

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

Calculate the right side:

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

Now, simplify the fraction [tex]\(\frac{24}{40}\)[/tex] by dividing both the numerator and the denominator by 8:

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

Therefore, the value of [tex]\(s\)[/tex] is [tex]\(\frac{3}{5}\)[/tex], which is also approximately 0.6.