Question

Emma wants to purchase a backpack for $32.00 and several notebooks, n, that cost
$4.50 each. She can spend no more than $50.00.
Which inequality and its solution represents her possible purchase?
A. 4.50n + 32 ≥ 50 n ≥ 4 B. 4.50n + 32 ≤ 50 n ≤ 4
C. 32n + 4.50 ≥ 50 n ≥ 1.8 D. 32n + 4.50 ≤ 50 n ≤ 1.8

Answer 1

To find the correct inequality representing Emma's possible purchase, we can set up the situation as follows:

Let \( n \) represent the number of notebooks.

The total cost of the backpack and the notebooks is given by:

\[
32.00 + 4.50n
\]

Emma can spend no more than $50.00, which gives us the inequality:

\[
32.00 + 4.50n \leq 50.00
\]

Now we can simplify this inequality:

1. Subtract 32 from both sides:

\[
4.50n \leq 50.00 - 32.00
\]

\[
4.50n \leq 18.00
\]

2. Divide both sides by 4.50:

\[
n \leq \frac{18.00}{4.50}
\]

\[
n \leq 4
\]

Thus the solution shows that Emma can buy **at most 4** notebooks.

Therefore, the correct inequality and its solution is:

**B.** \( 4.50n + 32 \leq 50 \) and \( n \leq 4 \)