Question
When a number is added to n plus StartFraction 1 Over 5 EndFraction n equals 24. of itself, the result is 24. The equation that models this problem is n + n plus StartFraction 1 Over 5 EndFraction n equals 24.n = 24. What is the value n?
n = 18
n = 20
n = 21n equals 23 and StartFraction Over 5 EndFraction 5
n = 23n equals 23 and StartFraction Over 5 EndFraction 5
n = 18
n = 20
n = 21n equals 23 and StartFraction Over 5 EndFraction 5
n = 23n equals 23 and StartFraction Over 5 EndFraction 5
Answers
Answered by
GPT-4o mini
The problem states that when a number \( n \) is added to itself plus \(\frac{1}{5}\) of itself, the total equals 24.
We can express this mathematically as follows:
\[
n + n + \frac{1}{5}n = 24
\]
Now combine the terms:
1. Combine the \( n \) terms:
\[
2n + \frac{1}{5}n = 24
\]
2. To combine \( 2n \) and \( \frac{1}{5}n \), we can express \( 2n \) with a common denominator:
\[
\frac{10}{5}n + \frac{1}{5}n = 24
\]
3. Now add the two fractions:
\[
\frac{10n + 1n}{5} = 24
\]
4. This simplifies to:
\[
\frac{11n}{5} = 24
\]
5. Next, multiply both sides by 5 to eliminate the fraction:
\[
11n = 120
\]
6. Then, solve for \( n \) by dividing both sides by 11:
\[
n = \frac{120}{11} \approx 10.91
\]
None of the options provided (18, 20, 21, 23) are correct since \( n = \frac{120}{11} \) does not equal any of those values. Please double-check the options or ensure that the problem setup reflects what you're asking about.
We can express this mathematically as follows:
\[
n + n + \frac{1}{5}n = 24
\]
Now combine the terms:
1. Combine the \( n \) terms:
\[
2n + \frac{1}{5}n = 24
\]
2. To combine \( 2n \) and \( \frac{1}{5}n \), we can express \( 2n \) with a common denominator:
\[
\frac{10}{5}n + \frac{1}{5}n = 24
\]
3. Now add the two fractions:
\[
\frac{10n + 1n}{5} = 24
\]
4. This simplifies to:
\[
\frac{11n}{5} = 24
\]
5. Next, multiply both sides by 5 to eliminate the fraction:
\[
11n = 120
\]
6. Then, solve for \( n \) by dividing both sides by 11:
\[
n = \frac{120}{11} \approx 10.91
\]
None of the options provided (18, 20, 21, 23) are correct since \( n = \frac{120}{11} \) does not equal any of those values. Please double-check the options or ensure that the problem setup reflects what you're asking about.