Question
Which of the following is a real-world problem that could be solved by calculating the sum 18+(−5)
18
+
(
−
5
)
?(1 point)
Responses
In the morning the temperature at Jackson’s house was 18°F. By noon is was 5 degrees warmer. What is the temperature at Jackson’s house now?
In the morning the temperature at Jackson’s house was 18°F. By noon is was 5 degrees warmer. What is the temperature at Jackson’s house now?
Jackson has $18 in his wallet. He puts in another $5 that his mom gives him. How much money does he have in his wallet now?
Jackson has $18 in his wallet. He puts in another $5 that his mom gives him. How much money does he have in his wallet now?
Jackson buys a meal for his family for $18. The next day his friend pays him back the $5 that he borrowed last week. How has the amount of money Jackson has changed over the course of these two transactions?
Jackson buys a meal for his family for $18. The next day his friend pays him back the $5 that he borrowed last week. How has the amount of money Jackson has changed over the course of these two transactions?
Jackson is on the second floor, which is 18 feet above ground. He then goes down some stairs, descending 5 feet. How many feet above ground is he now?
18
+
(
−
5
)
?(1 point)
Responses
In the morning the temperature at Jackson’s house was 18°F. By noon is was 5 degrees warmer. What is the temperature at Jackson’s house now?
In the morning the temperature at Jackson’s house was 18°F. By noon is was 5 degrees warmer. What is the temperature at Jackson’s house now?
Jackson has $18 in his wallet. He puts in another $5 that his mom gives him. How much money does he have in his wallet now?
Jackson has $18 in his wallet. He puts in another $5 that his mom gives him. How much money does he have in his wallet now?
Jackson buys a meal for his family for $18. The next day his friend pays him back the $5 that he borrowed last week. How has the amount of money Jackson has changed over the course of these two transactions?
Jackson buys a meal for his family for $18. The next day his friend pays him back the $5 that he borrowed last week. How has the amount of money Jackson has changed over the course of these two transactions?
Jackson is on the second floor, which is 18 feet above ground. He then goes down some stairs, descending 5 feet. How many feet above ground is he now?
Answers
GPT-4o mini
The problem that could be solved by calculating the sum \( 18 + (-5) \) is:
**"Jackson is on the second floor, which is 18 feet above ground. He then goes down some stairs, descending 5 feet. How many feet above ground is he now?"**
In this scenario, you would start at 18 feet (the initial height) and then subtract 5 feet (the distance descended), which corresponds to the calculation \( 18 + (-5) \).
**"Jackson is on the second floor, which is 18 feet above ground. He then goes down some stairs, descending 5 feet. How many feet above ground is he now?"**
In this scenario, you would start at 18 feet (the initial height) and then subtract 5 feet (the distance descended), which corresponds to the calculation \( 18 + (-5) \).
Carrie
Gracy is in an elevator in a parking garage where she is 32.8 feet below ground. She rides the elevator up 109.5 feet. Where is she now with respect to ground level?(1 point)
Responses
76.7 feet above ground
76.7 feet above ground
142.3 feet below ground
142.3 feet below ground
142.3 feet above ground
142.3 feet above ground
76.7 feet below ground
76.7 feet below ground
Responses
76.7 feet above ground
76.7 feet above ground
142.3 feet below ground
142.3 feet below ground
142.3 feet above ground
142.3 feet above ground
76.7 feet below ground
76.7 feet below ground
GPT-4o mini
To find Gracy's position with respect to ground level, you can use the following calculation:
1. Start with her initial position below ground: \(-32.8\) feet (since below ground is considered negative).
2. Then, add the distance she rides up: \( +109.5\) feet.
So, the calculation is:
\[
-32.8 + 109.5 = 76.7
\]
This means Gracy is now \(76.7\) feet above ground.
Therefore, the correct response is:
**76.7 feet above ground**.
1. Start with her initial position below ground: \(-32.8\) feet (since below ground is considered negative).
2. Then, add the distance she rides up: \( +109.5\) feet.
So, the calculation is:
\[
-32.8 + 109.5 = 76.7
\]
This means Gracy is now \(76.7\) feet above ground.
Therefore, the correct response is:
**76.7 feet above ground**.
Carrie
Determine the distance between −18.26
−
18.26
and −2.45
−
2.45
on a number line.(1 point)
Responses
20.71
20.71
−20.71
−
20.71
negative 20.71
−15.81
−
15.81
negative 15.81
15.81
−
18.26
and −2.45
−
2.45
on a number line.(1 point)
Responses
20.71
20.71
−20.71
−
20.71
negative 20.71
−15.81
−
15.81
negative 15.81
15.81
GPT-4o mini
To determine the distance between \(-18.26\) and \(-2.45\) on a number line, you can use the formula for distance between two points:
\[
\text{Distance} = |x_1 - x_2|
\]
Here, let \(x_1 = -18.26\) and \(x_2 = -2.45\).
Plugging in the values:
\[
\text{Distance} = |-18.26 - (-2.45)| = |-18.26 + 2.45| = |-18.26 + 2.45| = |-15.81| = 15.81
\]
So, the distance between \(-18.26\) and \(-2.45\) is **15.81**.
Therefore, the correct response is:
**15.81**.
\[
\text{Distance} = |x_1 - x_2|
\]
Here, let \(x_1 = -18.26\) and \(x_2 = -2.45\).
Plugging in the values:
\[
\text{Distance} = |-18.26 - (-2.45)| = |-18.26 + 2.45| = |-18.26 + 2.45| = |-15.81| = 15.81
\]
So, the distance between \(-18.26\) and \(-2.45\) is **15.81**.
Therefore, the correct response is:
**15.81**.
Carrie
Which context describes a difference of rational numbers?(1 point)
Responses
The team’s score did not change during the game.
The team’s score did not change during the game.
The team’s score increased when scoring.
The team’s score increased when scoring.
A football player loses yards on a play.
A football player loses yards on a play.
A football player gains yards on a play.
Responses
The team’s score did not change during the game.
The team’s score did not change during the game.
The team’s score increased when scoring.
The team’s score increased when scoring.
A football player loses yards on a play.
A football player loses yards on a play.
A football player gains yards on a play.
GPT-4o mini
The context that describes a difference of rational numbers is:
**"A football player loses yards on a play."**
In this case, losing yards can be represented as a negative change in score, reflecting a difference between the current position and the previous position. The other options primarily involve gains or no change, which do not represent a difference (especially not a negative difference).
**"A football player loses yards on a play."**
In this case, losing yards can be represented as a negative change in score, reflecting a difference between the current position and the previous position. The other options primarily involve gains or no change, which do not represent a difference (especially not a negative difference).
Carrie
Joey walked east for15 2/3 meters from home then he walked west for 21 3/4 meters how far was Joey from home
GPT-4o mini
To determine Joey's distance from home after walking, we need to calculate his total distance walked in each direction and then find the net displacement.
1. **Convert the mixed numbers to improper fractions**:
\[
15 \frac{2}{3} = \frac{15 \times 3 + 2}{3} = \frac{45 + 2}{3} = \frac{47}{3}
\]
\[
21 \frac{3}{4} = \frac{21 \times 4 + 3}{4} = \frac{84 + 3}{4} = \frac{87}{4}
\]
2. **Find a common denominator to subtract the distances**. The least common multiple of \(3\) and \(4\) is \(12\).
Convert \(\frac{47}{3}\) and \(\frac{87}{4}\) to have a denominator of \(12\):
\[
\frac{47}{3} = \frac{47 \times 4}{3 \times 4} = \frac{188}{12}
\]
\[
\frac{87}{4} = \frac{87 \times 3}{4 \times 3} = \frac{261}{12}
\]
3. **Determine the net distance walked**:
Joey walked east \( \frac{188}{12} \) meters and then walked west \( \frac{261}{12} \) meters. To find out how far he is from home:
\[
\text{Distance from home} = \text{Distance walked west} - \text{Distance walked east}
\]
\[
\text{Distance from home} = \frac{261}{12} - \frac{188}{12} = \frac{261 - 188}{12} = \frac{73}{12}
\]
4. **Convert back to a mixed number**:
\(\frac{73}{12}\) can be converted to a mixed number:
\[
73 \div 12 = 6 \quad \text{with a remainder of } 1
\]
Thus,
\[
\frac{73}{12} = 6 \frac{1}{12}
\]
Therefore, Joey is **6 \(\frac{1}{12}\) meters from home**.
1. **Convert the mixed numbers to improper fractions**:
\[
15 \frac{2}{3} = \frac{15 \times 3 + 2}{3} = \frac{45 + 2}{3} = \frac{47}{3}
\]
\[
21 \frac{3}{4} = \frac{21 \times 4 + 3}{4} = \frac{84 + 3}{4} = \frac{87}{4}
\]
2. **Find a common denominator to subtract the distances**. The least common multiple of \(3\) and \(4\) is \(12\).
Convert \(\frac{47}{3}\) and \(\frac{87}{4}\) to have a denominator of \(12\):
\[
\frac{47}{3} = \frac{47 \times 4}{3 \times 4} = \frac{188}{12}
\]
\[
\frac{87}{4} = \frac{87 \times 3}{4 \times 3} = \frac{261}{12}
\]
3. **Determine the net distance walked**:
Joey walked east \( \frac{188}{12} \) meters and then walked west \( \frac{261}{12} \) meters. To find out how far he is from home:
\[
\text{Distance from home} = \text{Distance walked west} - \text{Distance walked east}
\]
\[
\text{Distance from home} = \frac{261}{12} - \frac{188}{12} = \frac{261 - 188}{12} = \frac{73}{12}
\]
4. **Convert back to a mixed number**:
\(\frac{73}{12}\) can be converted to a mixed number:
\[
73 \div 12 = 6 \quad \text{with a remainder of } 1
\]
Thus,
\[
\frac{73}{12} = 6 \frac{1}{12}
\]
Therefore, Joey is **6 \(\frac{1}{12}\) meters from home**.