NASCAR Cup Car tires can weight as little as 24 pounds and as much as 28 pounds. The rubber of the tire weights 20.2 pounds and an inner liner weighs 0.65 pounds, how many inner liners can a team place in a tire?

Question

Part 1

If x represents the number of inner liners in the tire, which inequality statement represents the situation.

24 < 20.2 + 0.65x <28

20.2 + 0.65x ≤ 24 OR 20.2 + 0.65x ≥ 28

20.2 +0.65x <24 OR 20.2 + 0.65 > 28

24 ≤ 20.2 + 0.65x ≤28

Answer 1

To determine the number of inner liners that can be placed in a NASCAR Cup Car tire, let’s analyze the situation presented.

From the problem, we know:

• The minimum weight of the tire is 24 pounds.
• The maximum weight of the tire is 28 pounds.
• The weight of the rubber is 20.2 pounds.
• Each inner liner weighs 0.65 pounds.

We want to formulate an inequality that represents the total weight of the tire with added inner liners, represented by \(x\).

The total weight of the tire with \(x\) inner liners is given by: \[ \text{Total weight} = 20.2 + 0.65x \]

To find the range for \(x\), we need to set up an inequality that keeps the total weight between 24 and 28 pounds:

\[ 24 < 20.2 + 0.65x < 28 \]

Based on this, we can determine that the correct inequality statement that represents the situation is: \[ 24 < 20.2 + 0.65x < 28 \]

So, the correct choice is: 24 < 20.2 + 0.65x < 28.

Answer 2

Complete the statement based upon the solution to the inequality.

Teams can place no fewer than (blank) and no more than (blank) inner liners in the tires to meet the weight requirements.

Answer 3

To complete the statement based on the inequality \(24 < 20.2 + 0.65x < 28\), we need to solve the inequality for \(x\).

1. Lower Bound: \[ 20.2 + 0.65x > 24 \] Subtract 20.2 from both sides: \[ 0.65x > 3.8 \] Divide by 0.65: \[ x > \frac{3.8}{0.65} \approx 5.846 \] Since \(x\) must be a whole number (you can't have a fraction of an inner liner), this means: \[ x \geq 6 \]

2. Upper Bound: \[ 20.2 + 0.65x < 28 \] Subtract 20.2 from both sides: \[ 0.65x < 7.8 \] Divide by 0.65: \[ x < \frac{7.8}{0.65} \approx 12 \] So this means: \[ x \leq 11 \]

Now we can fill in the blanks:

Teams can place no fewer than 6 and no more than 11 inner liners in the tires to meet the weight requirements.

Answer 4

Let's put the entire problem in full.

Answer 5

Sure! Here’s the complete problem outlined clearly:

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Problem Statement:

NASCAR Cup Car tires can weigh as little as 24 pounds and as much as 28 pounds. The rubber of the tire weighs 20.2 pounds, and an inner liner weighs 0.65 pounds.

Questions:

1. Inequality Statement: If \( x \) represents the number of inner liners in the tire, which inequality statement represents the situation regarding the total weight of the tire?

   a) \( 24 < 20.2 + 0.65x < 28 \)

   b) \( 20.2 + 0.65x \leq 24 \) OR \( 20.2 + 0.65x \geq 28 \)

   c) \( 20.2 + 0.65x < 24 \) OR \( 20.2 + 0.65x > 28 \)

   d) \( 24 \leq 20.2 + 0.65x \leq 28 \)

   Correct Answer: a) \( 24 < 20.2 + 0.65x < 28 \)

2. Solution for Inner Liners: Complete the statement based upon the solution to the inequality.

   Teams can place no fewer than (blank) and no more than (blank) inner liners in the tires to meet the weight requirements.

   Answer: Teams can place no fewer than 6 and no more than 11 inner liners in the tires to meet the weight requirements.

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This summary incorporates the problem details, the derivation of the inequality statement, and the solution for the number of inner liners that can fit within the weight constraints. If you need further assistance or any additional details, feel free to ask!