Answer :
To figure out what percent of 175 is 7, we can set up a simple proportion. The idea is to find the percentage, [tex]\( p \)[/tex], that 7 represents out of 175. Here's a step-by-step breakdown of the process:
1. Set up the proportion: The phrase "what percent of 175 is 7" can be translated into a mathematical equation. We need to find a percentage, so we place 7 over 175 and set this equal to [tex]\( \frac{p}{100} \)[/tex]. This equation looks like this:
[tex]\[
\frac{7}{175} = \frac{p}{100}
\][/tex]
2. Solve for [tex]\( p \)[/tex]: To solve for the percentage [tex]\( p \)[/tex], you can use cross-multiplication. Multiply both sides in such a way you eliminate the fractions:
[tex]\[
7 \times 100 = 175 \times p
\][/tex]
Simplifying the left side, we get:
[tex]\[
700 = 175p
\][/tex]
3. Isolate [tex]\( p \)[/tex]: Divide both sides of the equation by 175 to solve for [tex]\( p \)[/tex]:
[tex]\[
p = \frac{700}{175}
\][/tex]
4. Calculate the value: Perform the division:
[tex]\[
p = 4
\][/tex]
So, 7 is 4% of 175.
With this in mind, let's go through the given options:
- A [tex]\(\frac{175}{7} = \frac{p}{100}\)[/tex]: This setup is incorrect because it does not properly represent "7 is p% of 175."
- B [tex]\(4\%\)[/tex]: This option is correct because we calculated that 7 is 4% of 175.
- C [tex]\(40\%\)[/tex]: This is incorrect as 7 is not 40% of 175.
- D [tex]\(\frac{7}{175} = \frac{p}{100}\)[/tex]: This equation is correct as it reflects the correct setup to find the percentage.
- E [tex]\(12.25\%\)[/tex]: This is incorrect since 7 is not 12.25% of 175.
- F [tex]\(25\%\)[/tex]: This is incorrect since 7 is not 25% of 175.
Thus, the correct answers are B [tex]\(4\%\)[/tex] and D [tex]\(\frac{7}{175} = \frac{p}{100}\)[/tex].
1. Set up the proportion: The phrase "what percent of 175 is 7" can be translated into a mathematical equation. We need to find a percentage, so we place 7 over 175 and set this equal to [tex]\( \frac{p}{100} \)[/tex]. This equation looks like this:
[tex]\[
\frac{7}{175} = \frac{p}{100}
\][/tex]
2. Solve for [tex]\( p \)[/tex]: To solve for the percentage [tex]\( p \)[/tex], you can use cross-multiplication. Multiply both sides in such a way you eliminate the fractions:
[tex]\[
7 \times 100 = 175 \times p
\][/tex]
Simplifying the left side, we get:
[tex]\[
700 = 175p
\][/tex]
3. Isolate [tex]\( p \)[/tex]: Divide both sides of the equation by 175 to solve for [tex]\( p \)[/tex]:
[tex]\[
p = \frac{700}{175}
\][/tex]
4. Calculate the value: Perform the division:
[tex]\[
p = 4
\][/tex]
So, 7 is 4% of 175.
With this in mind, let's go through the given options:
- A [tex]\(\frac{175}{7} = \frac{p}{100}\)[/tex]: This setup is incorrect because it does not properly represent "7 is p% of 175."
- B [tex]\(4\%\)[/tex]: This option is correct because we calculated that 7 is 4% of 175.
- C [tex]\(40\%\)[/tex]: This is incorrect as 7 is not 40% of 175.
- D [tex]\(\frac{7}{175} = \frac{p}{100}\)[/tex]: This equation is correct as it reflects the correct setup to find the percentage.
- E [tex]\(12.25\%\)[/tex]: This is incorrect since 7 is not 12.25% of 175.
- F [tex]\(25\%\)[/tex]: This is incorrect since 7 is not 25% of 175.
Thus, the correct answers are B [tex]\(4\%\)[/tex] and D [tex]\(\frac{7}{175} = \frac{p}{100}\)[/tex].
