6. A student wants to purchase some new school supplies. He wants to buy a calculator that costs $24 and some notebooks for school. Each notebook costs $2. The student only has $37 to spend.

Question

Let n represent the number of notebooks that he buys.

Which inequality describes this scenario?

(1 point)
Responses

37≥2n+2437 is greater than or equal to 2 n plus 24

24n+2≥3724 n plus 2 is greater than or equal to 37

37<2n+2437<2n+24

37>2n+24

Answer 1

To determine the correct inequality that describes the student's situation, let's break down the costs involved.

1. The calculator costs $24.
2. Each notebook costs $2, so buying \( n \) notebooks will cost \( 2n \).
3. The total cost for the calculator and the notebooks will be \( 24 + 2n \).
4. The student has a total of $37 to spend.

The student wants to ensure that the total cost does not exceed $37. Therefore, we can represent this as:

\[ 24 + 2n \leq 37 \]

To express this inequality in a standard form, we can rearrange it:

1. Subtract 24 from both sides: \[ 2n \leq 37 - 24 \]

2. Simplifying the right side gives: \[ 2n \leq 13 \]

This inequality indicates that the total spending should be less than or equal to what the student has, which reflects the condition that they should not exceed their budget.

From the options provided:

• 37 ≥ 2n + 24 → This can be rewritten as 2n + 24 ≤ 37, which is correct.
• 24n + 2 ≥ 37 → Incorrect, as it misrepresents the relationship.
• 37 < 2n + 24 → Incorrect as it suggests they want to exceed their budget.
• 37 > 2n + 24 → This is equivalent to 2n + 24 ≤ 37, which is the form we derived.

So, the correct inequality is represented as:

37 ≥ 2n + 24.