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>28.8
n greater than 28.8

n>15
n greater than 15

n>45

Answer 1

Let's first write the inequality based on the problem statement.

The statement says "twelve less than four-fifths of a number is more than 24." We can express this mathematically as follows:

Let \( n \) be the number. Then, four-fifths of \( n \) is \( \frac{4}{5}n \).

The inequality can be written as:

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

Next, we'll solve the 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 \( n \):

\[ n > 36 \times \frac{5}{4} \]

\[ n > 36 \times 1.25 \]

\[ n > 45 \]

Therefore, the solution to Lucia's inequality is:

\[ n > 45 \]

So the correct response is:

n > 45 (n greater than 45)