Question

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 4/5n−12>24 , where n equals the number, to help solve this problem. Solve her inequality.

Answer 1

To solve the inequality \( \frac{4}{5}n - 12 > 24 \), we can follow these steps:

1. **Add 12 to both sides**:

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

This simplifies to:

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

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

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

Calculating \( 36 \times \frac{5}{4} \):

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

So we have:

\[
n > 45
\]

Thus, the solution to the inequality is

\[
\boxed{(45, \infty)}
\]

This means all values of \( n \) that are greater than 45 satisfy the original inequality.