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

Question

Responses

n>28.8
n greater than 28.8

n>15
n greater than 15

n>45
n greater than 45

n>9.6
n greater than 9.6

Answer 1

To solve the problem, we start with the statement given. Let's denote the unknown number as \( n \).

The phrase "four-fifths of a number" translates to \( \frac{4}{5}n \). Therefore, "twelve less than four-fifths of a number" can be expressed mathematically as:

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

We know that this expression is more than 24, which translates to the inequality:

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

Now we can 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 isolate \( n \): \[ n > 36 \cdot \frac{5}{4} \] \[ n > 45 \]

Thus, the solution to the inequality is:

\[ n > 45 \]

Based on the response options provided, the correct answer is:

n>45
n greater than 45