Which of the questions below can be answered using the sum -12 + 10? Check all that apply.

AAt 6:00 a.m., the temperature was -12 degrees Fahrenheit. Two hours later, the temperature was 10 degrees warmer. What was the temperature at 8:00 a.m.?
BWhile playing the Integer Game, Richard's hand had a value of -12, and Jason's hand had a value of 10. How many more points did Jason have than Richard?
CHarper owed her mother $10. In order to go to the movies, she had to borrow another $12 from her mother. How much does Harper owe her mother now?
DA quarterback lost 12 yards on first down but then gained 10 yards on second down. What is the quarterback's total number of yards?

Question

06-11-2026
Mathematics

Answered

Which of the questions below can be answered using the sum -12 + 10? Check all that apply.

AAt 6:00 a.m., the temperature was -12 degrees Fahrenheit. Two hours later, the temperature was 10 degrees warmer. What was the temperature at 8:00 a.m.?
BWhile playing the Integer Game, Richard's hand had a value of -12, and Jason's hand had a value of 10. How many more points did Jason have than Richard?
CHarper owed her mother $10. In order to go to the movies, she had to borrow another $12 from her mother. How much does Harper owe her mother now?
DA quarterback lost 12 yards on first down but then gained 10 yards on second down. What is the quarterback's total number of yards?

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-06T01:51:11-05:00

The expression $-12 + 10$ represents situations involving an initial value of $-12$ followed by an increase of $10$.
Scenario 1 describes a temperature of $-12^\circ$ increasing by $10^\circ$, which is $-12 + 10$.
Scenario 4 describes a loss of $12$ yards ($-12$) followed by a gain of $10$ yards ($+10$), resulting in $-12 + 10$.
The correct scenarios are the first and the fourth.
$\boxed{\text{Scenario 1 and Scenario 4}}$

Explanation

Analyzing the Scenarios

To identify which scenarios are represented by the expression $-12 + 10$, we need to translate each word problem into a mathematical operation using positive and negative integers to represent gain/loss, temperature change, or debt. We evaluate each scenario one by one.

Evaluating Each Scenario

Scenario 1: The temperature started at $-12^\circ\text{F}$ and rose by $10^\circ\text{F}$. A rise in temperature is represented by addition. Therefore, the new temperature is $-12 + 10$. This scenario matches the expression.

Scenario 2: Richard's score is $-12$ and Jason's is $10$. To find how many more points Jason has, we calculate the difference, which is $10 - (-12)$. This is equivalent to $10 + 12$, not $-12 + 10$.

Scenario 3: Harper already owes $\$10$ (a debt of $-10$) and borrows another $\$12$ (another debt of $-12$). The total amount she owes is $-10 + (-12) = -22$. This does not match the expression.

Scenario 4: The quarterback lost $12$ yards (represented as $-12$) and gained $10$ yards (represented as $+10$). The net yardage is $-12 + 10$. This scenario matches the expression.

Concluding the Answer

Comparing our translations to the original expression $-12 + 10$, we see that Scenario 1 and Scenario 4 both result in the mathematical expression $-12 + 10$. The correct scenarios are the first one regarding temperature and the last one regarding football yardage. Final answer is scenario 1 and scenario 4.

Examples

Understanding how to translate word problems into mathematical expressions is crucial for solving real-world problems. For instance, in finance, if you have a bank account balance of $\$50$ and you pay a bill of $\$60$, your new balance is $50 - 60 = -\$10$, representing an overdraft. Similarly, in navigation, if a ship moves $5$ miles north and then $8$ miles south, its displacement from the starting point is $5 - 8 = -3$ miles south. Mastering these operations helps in tracking progress, finances, and physical changes accurately.