DIGITAL Math Integers Word Problems Google Slides Worksheet with ... - Free Printable

The image contains a set of integer word problems with an answer key. Below, I will explain the solutions to each problem step by step.

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Problem 1:

Question: The temperature was $72^\circ$ and dropped $15^\circ$. What was the temperature after the change?

Solution:
- Initial temperature: $72^\circ$
- Temperature drop: $-15^\circ$
- Final temperature = Initial temperature + Temperature change
\[
72 + (-15) = 72 - 15 = 57
\]

Answer: $\boxed{57}$

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Problem 2:

Question: On the first play, the football team lost $5$ yards. On the second play, the team lost $3$ more yards. What was their total change in yards?

Solution:
- Change on the first play: $-5$ yards
- Change on the second play: $-3$ yards
- Total change = Sum of changes
\[
-5 + (-3) = -5 - 3 = -8
\]

Answer: $\boxed{-8}$

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Problem 3:

Question: An elevator started on the first floor and went up $19$ floors. It then came down $11$ floors. What floor is it on now?

Solution:
- Starting floor: $1$
- Floors up: $+19$
- Floors down: $-11$
- Final floor = Starting floor + Floors up + Floors down
\[
1 + 19 + (-11) = 1 + 19 - 11 = 9
\]

Answer: $\boxed{9}$

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Problem 4:

Question: A submarine is $60$ feet below sea level. The submarine then rises $16$ feet and then descends $40$ feet. How many feet is the submarine below sea level?

Solution:
- Initial depth: $-60$ feet (below sea level)
- Rise: $+16$ feet
- Descent: $-40$ feet
- Final depth = Initial depth + Rise + Descent
\[
-60 + 16 + (-40) = -60 + 16 - 40 = -84
\]

Answer: $\boxed{-84}$

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Problem 5:

Question: You are at an elevation of $6,000$ feet. You look down to an elevation of $5,650$ feet. What is your change in elevation?

Solution:
- Initial elevation: $6,000$ feet
- Final elevation: $5,650$ feet
- Change in elevation = Final elevation - Initial elevation
\[
5,650 - 6,000 = -350
\]

Answer: $\boxed{-350}$

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Problem 6:

Question: At midnight, the temperature was $30^\circ$. By $6:00$ a.m., it dropped $9^\circ$, and by noon, it increased by $17^\circ$. What was the temperature at noon?

Solution:
- Midnight temperature: $30^\circ$
- Drop by $6:00$ a.m.: $-9^\circ$
- Increase by noon: $+17^\circ$
- Noon temperature = Midnight temperature + Drop + Increase
\[
30 + (-9) + 17 = 30 - 9 + 17 = 38
\]

Answer: $\boxed{38}$

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Problem 7:

Question: The main control of a building is in the basement. A clerk starts going up $12$ floors, then goes down $4$ floors, and finally goes up $3$ floors. What floor is the clerk on?

Solution:
- Starting floor: $-1$ (basement)
- Up $12$ floors: $+12$
- Down $4$ floors: $-4$
- Up $3$ floors: $+3$
- Final floor = Starting floor + Up $12$ + Down $4$ + Up $3$
\[
-1 + 12 + (-4) + 3 = -1 + 12 - 4 + 3 = 10
\]

Answer: $\boxed{10}$

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Problem 8:

Question: A submarine starts at the surface of the Pacific Ocean and descends $60$ feet per hour. With a whole number expression, describe how many feet it will descend after $6$ hours.

Solution:
- Rate of descent: $60$ feet per hour
- Time: $6$ hours
- Total descent = Rate × Time
\[
60 \times 6 = 360
\]

Answer: $\boxed{360}$

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Problem 9:

Question: A skydiver falls approximately $10$ meters per second. Write a whole number expression to show how many meters he will fall in $40$ seconds.

Solution:
- Rate of fall: $10$ meters per second
- Time: $40$ seconds
- Total distance fallen = Rate × Time
\[
10 \times 40 = 400
\]

Answer: $\boxed{400}$

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Problem 10:

Question: A freight train is $0$ miles per hour. After $15$ minutes, it is traveling $70$ miles per hour. What integer represents the average increase in speed per minute?

Solution:
- Initial speed: $0$ miles per hour
- Final speed: $70$ miles per hour
- Time elapsed: $15$ minutes
- Increase in speed = Final speed - Initial speed
\[
70 - 0 = 70 \text{ miles per hour}
\]
- Average increase per minute = Increase in speed ÷ Time elapsed
\[
\frac{70}{15} = \frac{14}{3} \approx 4.67 \text{ miles per hour per minute}
\]
- Since the question asks for an integer, we round to the nearest whole number:
\[
\boxed{5}
\]

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Final Answers:

1. $\boxed{57}$
2. $\boxed{-8}$
3. $\boxed{9}$
4. $\boxed{-84}$
5. $\boxed{-350}$
6. $\boxed{38}$
7. $\boxed{10}$
8. $\boxed{360}$
9. $\boxed{400}$
10. $\boxed{5}$

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Boxed Final Answer:
\[
\boxed{57, -8, 9, -84, -350, 38, 10, 360, 400, 5}
\]