Twelve less than four-fifths of a number is more than 24. What are all the possible values of the number? Lucia wrote the inequality 45n−12>24

Question

, where n equals the number, to help solve this problem. Solve her inequality.(1 point)
Responses

n>9.6
n greater than 9.6

n>45
n greater than 45

n>15
n greater than 15

n>28.8

Answer 1

To solve the original problem, let's first restate the inequality based on the description given.

The problem states that "twelve less than four-fifths of a number is more than 24." We can express this mathematically.

Let \(n\) be the number. The expression "four-fifths of a number" can be written as \(\frac{4}{5}n\). Therefore, "twelve less than four-fifths of a number" can be expressed as \(\frac{4}{5}n - 12\).

Now, setting up the inequality we have:

\[ \frac{4}{5}n - 12 > 24 \]

Next, we'll solve this inequality step-by-step.

1. Add 12 to both sides: \[ \frac{4}{5}n > 24 + 12 \] \[ \frac{4}{5}n > 36 \]

2. Now, multiply both sides by \(\frac{5}{4}\) to isolate \(n\): \[ n > 36 \cdot \frac{5}{4} \] \[ n > 45 \]

So, the solution to the inequality is: \[ n > 45 \]

Thus, the correct response based on the calculations is:

n > 45

This indicates that the number must be greater than 45.