Adding and Subtracting Integers Word Problems Worksheet | PDF ... - Free Printable

Problem Analysis and Solutions

The provided worksheet involves word problems that require adding and subtracting integers. Let's solve each problem step by step.

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#### Problem 1:
Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level. What is the difference between these two elevations?

- Step 1: Identify the elevations.
- Mt. Everest: \( +29,028 \) feet (above sea level)
- Dead Sea: \( -1,312 \) feet (below sea level)

- Step 2: To find the difference between these two elevations, we calculate:
\[
\text{Difference} = \text{Elevation of Mt. Everest} - \text{Elevation of Dead Sea}
\]
\[
\text{Difference} = 29,028 - (-1,312)
\]

- Step 3: Subtracting a negative number is equivalent to adding its positive counterpart:
\[
29,028 - (-1,312) = 29,028 + 1,312
\]

- Step 4: Perform the addition:
\[
29,028 + 1,312 = 30,340
\]

- Final Answer:
\[
\boxed{30,340}
\]

---

#### Problem 2:
In Buffalo, New York, the temperature was \(-14^\circ F\) in the morning. If the temperature dropped \(7^\circ F\), what is the temperature now?

- Step 1: Identify the initial temperature and the change in temperature.
- Initial temperature: \( -14^\circ F \)
- Temperature drop: \( -7^\circ F \)

- Step 2: To find the new temperature, subtract the drop from the initial temperature:
\[
\text{New Temperature} = \text{Initial Temperature} + \text{Temperature Drop}
\]
\[
\text{New Temperature} = -14 + (-7)
\]

- Step 3: Adding two negative numbers results in a larger negative number:
\[
-14 + (-7) = -21
\]

- Final Answer:
\[
\boxed{-21}
\]

---

#### Problem 3:
A submarine was situated 800 feet below sea level. If it ascends 250 feet, what is its new position?

- Step 1: Identify the initial position and the change in position.
- Initial position: \( -800 \) feet (below sea level)
- Ascension: \( +250 \) feet

- Step 2: To find the new position, add the ascension to the initial position:
\[
\text{New Position} = \text{Initial Position} + \text{Ascension}
\]
\[
\text{New Position} = -800 + 250
\]

- Step 3: Perform the addition:
\[
-800 + 250 = -550
\]

- Final Answer:
\[
\boxed{-550}
\]

---

#### Problem 4:
In the Sahara Desert one day it was \(136^\circ F\). In the Gobi Desert a temperature of \(-50^\circ F\) was recorded. What is the difference between these two temperatures?

- Step 1: Identify the temperatures.
- Sahara Desert: \( +136^\circ F \)
- Gobi Desert: \( -50^\circ F \)

- Step 2: To find the difference between these two temperatures, calculate:
\[
\text{Difference} = \text{Temperature in Sahara Desert} - \text{Temperature in Gobi Desert}
\]
\[
\text{Difference} = 136 - (-50)
\]

- Step 3: Subtracting a negative number is equivalent to adding its positive counterpart:
\[
136 - (-50) = 136 + 50
\]

- Step 4: Perform the addition:
\[
136 + 50 = 186
\]

- Final Answer:
\[
\boxed{186}
\]

---

#### Problem 5:
Your checking account is overdrawn by \$50. You write a check for \$20. What is the balance in your account?

- Step 1: Identify the initial balance and the transaction.
- Initial balance: \( -\$50 \) (overdrawn)
- Check written: \( -\$20 \) (additional withdrawal)

- Step 2: To find the new balance, add the check amount to the initial balance:
\[
\text{New Balance} = \text{Initial Balance} + \text{Check Amount}
\]
\[
\text{New Balance} = -50 + (-20)
\]

- Step 3: Adding two negative numbers results in a larger negative number:
\[
-50 + (-20) = -70
\]

- Final Answer:
\[
\boxed{-70}
\]

---

Final Answers:

1. \(\boxed{30,340}\)
2. \(\boxed{-21}\)
3. \(\boxed{-550}\)
4. \(\boxed{186}\)
5. \(\boxed{-70}\)