Question

line in the image represents the cars gas tank. based on the image, sort each of the statements that are true (left) and false (right). true evidence 6 items false when the gas tank is full, it holds 12 gallons. half a tank of gas in her dads car is 12 gallons. when the gas tank is full, it holds 24 gallons. a gas tank that holds 50 percent more gas would hold 24 gallons. half a tank of gas in her dads car is 6 gallons. a gas tank that holds 50 percent more gas would hold 18 gallons.

Explanation:

To solve this, we analyze each statement using the fact that a full tank holds 12 gallons (from the first statement, which we can take as given for analysis):

Step 1: Analyze "When the gas tank is full, it holds 12 gallons."

This is the base fact (given as part of the problem’s context for analysis), so it’s True.

Step 2: Analyze "Half a tank of gas in her dad’s car is 12 gallons."

Half of 12 gallons is \( \frac{12}{2} = 6 \) gallons, not 12. So this is False.

Step 3: Analyze "When the gas tank is full, it holds 24 gallons."

The base fact says a full tank is 12 gallons, so 24 is incorrect. This is False.

Step 4: Analyze "A gas tank that holds 50 percent more gas would hold 24 gallons."

50% more than 12 gallons: \( 12 + 0.5(12) = 12 + 6 = 18 \) gallons, not 24. Wait, no—wait, if the original is 12, 50% more is \( 12 \times 1.5 = 18 \). Wait, no, the statement says "would hold 24 gallons"—this is incorrect. Wait, no, maybe I misread. Wait, if the original full tank is 12, 50% more is \( 12 + 6 = 18 \), so 24 is wrong. Wait, no, maybe the original is 16? No, the first statement says full is 12. So this is False? Wait, no, wait: Wait, maybe the first statement is "When the gas tank is full, it holds 12 gallons" (True). Then "Half a tank is 6 gallons" (so "Half a tank is 12 gallons" is False). "Full is 24" is False. "50% more than 12 is 18, so 'holds 24' is False". "Half a tank is 6 gallons" (True). "50% more than 12 is 18, so 'holds 18' is True". Wait, let's re-express:

• Full tank = 12 gallons (True, from first statement).
• Half tank: \( \frac{12}{2} = 6 \) gallons (so "Half a tank is 6 gallons" is True).
• 50% more than 12: \( 12 \times 1.5 = 18 \) gallons (so "A gas tank that holds 50 percent more gas would hold 18 gallons" is True).

Correct Sorting:

True Statements:

• When the gas tank is full, it holds 12 gallons.
• Half a tank of gas in her dad’s car is 6 gallons.
• A gas tank that holds 50 percent more gas would hold 18 gallons.

False Statements:

• Half a tank of gas in her dad’s car is 12 gallons.
• When the gas tank is full, it holds 24 gallons.
• A gas tank that holds 50 percent more gas would hold 24 gallons.

(Note: The problem’s "Evidence" list includes these 6 statements, so we sort each:

• True:
• When the gas tank is full, it holds 12 gallons.
• Half a tank of gas in her dad’s car is 6 gallons.
• A gas tank that holds 50 percent more gas would hold 18 gallons.

• False:
• Half a tank of gas in her dad’s car is 12 gallons.
• When the gas tank is full, it holds 24 gallons.
• A gas tank that holds 50 percent more gas would hold 24 gallons.

)

Answer:

To solve this, we analyze each statement using the fact that a full tank holds 12 gallons (from the first statement, which we can take as given for analysis):

Step 1: Analyze "When the gas tank is full, it holds 12 gallons."

This is the base fact (given as part of the problem’s context for analysis), so it’s True.

Step 2: Analyze "Half a tank of gas in her dad’s car is 12 gallons."

Half of 12 gallons is \( \frac{12}{2} = 6 \) gallons, not 12. So this is False.

Step 3: Analyze "When the gas tank is full, it holds 24 gallons."

The base fact says a full tank is 12 gallons, so 24 is incorrect. This is False.

Step 4: Analyze "A gas tank that holds 50 percent more gas would hold 24 gallons."

50% more than 12 gallons: \( 12 + 0.5(12) = 12 + 6 = 18 \) gallons, not 24. Wait, no—wait, if the original is 12, 50% more is \( 12 \times 1.5 = 18 \). Wait, no, the statement says "would hold 24 gallons"—this is incorrect. Wait, no, maybe I misread. Wait, if the original full tank is 12, 50% more is \( 12 + 6 = 18 \), so 24 is wrong. Wait, no, maybe the original is 16? No, the first statement says full is 12. So this is False? Wait, no, wait: Wait, maybe the first statement is "When the gas tank is full, it holds 12 gallons" (True). Then "Half a tank is 6 gallons" (so "Half a tank is 12 gallons" is False). "Full is 24" is False. "50% more than 12 is 18, so 'holds 24' is False". "Half a tank is 6 gallons" (True). "50% more than 12 is 18, so 'holds 18' is True". Wait, let's re-express:

• Full tank = 12 gallons (True, from first statement).
• Half tank: \( \frac{12}{2} = 6 \) gallons (so "Half a tank is 6 gallons" is True).
• 50% more than 12: \( 12 \times 1.5 = 18 \) gallons (so "A gas tank that holds 50 percent more gas would hold 18 gallons" is True).

Correct Sorting:

True Statements:

• When the gas tank is full, it holds 12 gallons.
• Half a tank of gas in her dad’s car is 6 gallons.
• A gas tank that holds 50 percent more gas would hold 18 gallons.

False Statements:

• Half a tank of gas in her dad’s car is 12 gallons.
• When the gas tank is full, it holds 24 gallons.
• A gas tank that holds 50 percent more gas would hold 24 gallons.

(Note: The problem’s "Evidence" list includes these 6 statements, so we sort each:

• True:
• When the gas tank is full, it holds 12 gallons.
• Half a tank of gas in her dad’s car is 6 gallons.
• A gas tank that holds 50 percent more gas would hold 18 gallons.

• False:
• Half a tank of gas in her dad’s car is 12 gallons.
• When the gas tank is full, it holds 24 gallons.
• A gas tank that holds 50 percent more gas would hold 24 gallons.

)