Four-fifths of a number minus 12 is more than 24.85. What are all the possible values of the number? Write an inequality that could be used to solve this problem.

Question

12 - 4/5n <_ 24.85, when n is equal to the number

4/5n - 12 <_ 24.85, where n is equal to the number

4/5n - 12 > 24.85, where n is equal to the number

12 - 4/5n > 24.85, where n is equal to the number

Answer 1

To translate the problem statement into a mathematical inequality, we start with the phrase "Four-fifths of a number minus 12 is more than 24.85." This can be expressed as:

\[ \frac{4}{5}n - 12 > 24.85 \]

This is the correct inequality that represents the situation described in the problem.

Now let's analyze the other options provided:

1. 12 - \(\frac{4}{5}n \leq 24.85\): This does not match the original statement because it involves a less than or equal to condition.

2. \(\frac{4}{5}n - 12 \leq 24.85\): This also does not match as it introduces a less than or equal to condition.

3. \(\frac{4}{5}n - 12 > 24.85\): This is the same as our derived inequality and is indeed correct.

4. 12 - \(\frac{4}{5}n > 24.85\): This is incorrect as it flips the operations and relationship.

Thus, the correct inequality that could be used to solve the problem is:

\[ \frac{4}{5}n - 12 > 24.85 \]

Now let's solve the inequality:

1. Start by adding 12 to both sides: \[ \frac{4}{5}n > 24.85 + 12 \] \[ \frac{4}{5}n > 36.85 \]

2. Now, multiply both sides by \(\frac{5}{4}\) to isolate \(n\): \[ n > 36.85 \times \frac{5}{4} \] \[ n > 36.85 \times 1.25 \] \[ n > 46.0625 \]

Thus, the possible values of \(n\) are all numbers greater than approximately \(46.0625\).