Let's solve the problem step by step.
1. Understanding the Problem:
- Alex has 70% of her weekly paycheck automatically deposited into a savings account.
- The amount deposited this week is $35.
- We need to find the total amount of Alex's paycheck, denoted as [tex]\( p \)[/tex].
2. Setting up the Mathematical Equation:
- Since 70% of Alex's paycheck [tex]\( p \)[/tex] is deposited into her savings account, we can represent this mathematically as:
[tex]\[
0.70 \times p = 35
\][/tex]
- To find [tex]\( p \)[/tex], we need to solve this equation.
3. Rewriting the Percentage Equation:
- The equation [tex]\( 0.70 \times p = 35 \)[/tex] can be rewritten using fractions. 70% is equivalent to [tex]\( \frac{70}{100} \)[/tex]:
[tex]\[
\frac{70}{100} \times p = 35
\][/tex]
4. Formulating the Correct Option:
- We need to compare this equation with the options given.
Among the given options, we need one that mathematically portrays the relationship [tex]\( \frac{70}{100} \times p = 35 \)[/tex]. Let's assess each option:
- Option 1: [tex]\( \frac{p}{70} = \frac{35}{100} \)[/tex]
- Rearranging doesn't yield the correct relationship between [tex]\( p \)[/tex], 70%, and 35 dollars.
- Option 2: [tex]\( \frac{35}{p} = \frac{70}{100} \)[/tex]
- This option incorrectly positions the variables.
- Option 3: [tex]\( \frac{p}{35} = \frac{70}{100} \)[/tex]
- This again doesn't correctly frame the percentage relationship in the form we need.
- Option 4: [tex]\( \frac{70}{p} = \frac{35}{100} \)[/tex]
- This correctly represents the original equation when solved by cross-multiplying.
[tex]\[
\frac{70}{p} = \frac{35}{100}
\][/tex]
Thus, the correct equation that shows how to find [tex]\( p \)[/tex], the total amount of Alex's paycheck, is:
[tex]\[
\boxed{\frac{70}{p} = \frac{35}{100}}
\][/tex]
