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.(1 point)

Question

Responses

n>15
  n greater than 15

n>28.8
  n greater than 28.8

n>9.6
  n greater than 9.6

n>45

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

3. Calculate \( 36 \times \frac{5}{4} \): \[ 36 \times \frac{5}{4} = 36 \times 1.25 = 45 \]

Thus, we have: \[ n > 45 \]

The final answer is: \[ n > 45 \]

Therefore, the correct response is:

• \( n > 45 \) (n greater than 45).