Questions: Suzanne was given a 50 gift card to a store. With the money on the gift card, Suzanne was able to buy n shirts that cost 8 each. Which of the following must be true? 50/n ≤ 8 50/n ≥ 8 50/8n ≤ 0 50-8n ≤ 0

Suzanne was given a 50 gift card to a store. With the money on the gift card, Suzanne was able to buy n shirts that cost 8 each. Which of the following must be true?
50/n ≤ 8
50/n ≥ 8
50/8n ≤ 0
50-8n ≤ 0

Transcript text: Next-Generation Quantitative Reasoning, Algebra, and Statistics - Question 13 of 20 Instructions Choose the best answer. If necessary, use the paper you were given Question Suzanne was given a $\$ 50$ gift card to a store. With the money on the gift card, Suzanne was able to buy $n$ shirts that cost $\$ 8$ each. Which of the following must be true? $\frac{50}{n} \leq 8$ $\frac{50}{n} \geq 8$ $\frac{50}{8 n} \leq 0$ $50-8 n \leq 0$

Solution

Solution Steps

To determine which of the given inequalities must be true, we need to analyze the relationship between the total amount on the gift card, the cost per shirt, and the number of shirts Suzanne can buy.

Suzanne has a $50 gift card.
Each shirt costs $8.
Suzanne buys $ n $ shirts.

The total cost for $ n $ shirts is $ 8n $. This total cost must be less than or equal to the amount on the gift card, which is $50. Therefore, the inequality $ 8n \leq 50 $ must hold true. We can rearrange this inequality to match one of the given options.

Solution Approach

Calculate the total cost for $ n $ shirts.
Set up the inequality $ 8n \leq 50 $.
Rearrange the inequality to match one of the given options.

Step 1: Determine the Total Cost for $ n $ Shirts

Given:

Gift card amount: $ \$50 $
Cost per shirt: $ \$8 $

The total cost for $ n $ shirts is $ 8n $.

Step 2: Set Up the Inequality

The total cost must be less than or equal to the gift card amount: \[ 8n \leq 50 \]

Step 3: Rearrange the Inequality

To match one of the given options, we rearrange the inequality: \[ 50 - 8n \geq 0 \]

Step 4: Verify the Inequality

From the Python output, we calculated $ n = 6 $. Substituting $ n = 6 $ into the inequality: \[ 50 - 8 \times 6 = 50 - 48 = 2 \] Since $ 2 \geq 0 $, the inequality holds true.

Final Answer

$\boxed{50 - 8n \geq 0}$

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