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

Question

Responses

n>45
n greater than 45

n>28.8
n greater than 28.8

n>9.6
n greater than 9.6

n>15

Answer 1

To solve the inequality, we start with the expression based on the problem statement:

"twelve less than four-fifths of a number is more than 24."

This can be mathematically represented as:

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

Next, we will solve this inequality step by step.

1. Add 12 to both sides:

\[ \frac{4}{5}n > 24 + 12 \] \[ \frac{4}{5}n > 36 \]

2. Multiply both sides by \( \frac{5}{4} \) to solve for \( n \):

\[ n > 36 \cdot \frac{5}{4} \] \[ n > 36 \cdot 1.25 \] \[ n > 45 \]

So, the solution to the inequality is:

\[ n > 45 \]

Therefore, the response is:

n > 45
n greater than 45