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>15
n greater than 15

n>9.6
n greater than 9.6

n>45
n greater than 45

n>28.8

Answer 1

Let's start by interpreting the statement: "Twelve less than four-fifths of a number is more than 24."

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:

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

We need to set up the inequality:

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

Now, add \( 12 \) to both sides:

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

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

Next, to isolate \( n \), multiply both sides by \( \frac{5}{4} \):

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

Calculating the right side:

\[ 36 \times \frac{5}{4} = 36 \times 1.25 = 45 \]

Thus, we have:

\[ n > 45 \]

So, the correct answer is:

n > 45