Let's solve each of these integer word problems step by step, showing all work and using proper labels.
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1) Julian is moving from his hometown of Sedona, Arizona, to Juneau, Alaska. He knows he is going to face a big temperature change, and he is getting ready. The hottest it gets in Sedona is 112 degrees F. The hottest it gets in Juneau is 72 degrees F. Approximately what temperature change will Julian experience?
Solution:
We need to find the
difference in temperature between Sedona and Juneau.
- Sedona’s hottest temperature:
112°F
- Juneau’s hottest temperature:
72°F
Temperature change = Temperature in Sedona − Temperature in Juneau
= 112 − 72
=
40°F
Since Julian is moving from a warmer place to a cooler one, the
temperature decreases by 40°F.
✔ Answer: Julian will experience a temperature change of
−40°F (a decrease of 40 degrees).
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2) Abraham is spending a day at the hotel pool. He enjoys jumping from the very cool pool (62 degrees) to the very hot Jacuzzi (113 degrees). What temperature change is Abraham experiencing as he moves from pool to Jacuzzi?
Solution:
We are finding the change from the pool to the Jacuzzi.
- Pool temperature:
62°F
- Jacuzzi temperature:
113°F
Temperature change = Jacuzzi temp − Pool temp
= 113 − 62
=
51°F
This is an
increase in temperature.
✔ Answer: Abraham experiences a temperature change of
+51°F.
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3) Zack just got a grade of 93 on a report. However, because he turned it in late, his teacher is going to deduct 15 points. What will Zack’s final score on the report be?
Solution:
Original grade:
93
Points deducted:
15
Final score = 93 − 15
=
78
✔ Answer: Zack’s final score will be
78.
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4) On Monday, Taylor lost 20 dollars to Zack when playing a card game. He was angry that he had lost, so he kept playing. On Tuesday, Taylor lost another 5 dollars. On Wednesday, he neither lost nor won. On Thursday Taylor lost another 7 dollars. By then, Taylor had lost all of his savings. How much money did Taylor have before he started playing?
Solution:
We are told that Taylor
lost all his savings by Thursday. That means the total amount he lost equals how much he started with.
Add up all the losses:
- Monday: −$20
- Tuesday: −$5
- Wednesday: $0 (no change)
- Thursday: −$7
Total loss = 20 + 5 + 7 =
$32
So, Taylor must have started with
$32.
✔ Answer: Taylor had
$32 before he started playing.
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5) Imani got a notice from the bank saying that she had overspent, so her account balance was -$43. She wrote an additional check for $50 after she overdrawn her account. What will be Imani’s bank account balance once the new check goes through?
Solution:
Current balance:
−$43 (overdraft)
She writes a check for
$50, which means she spends another $50.
New balance = Current balance − $50
= −43 − 50
=
−93
✔ Answer: Imani’s new bank account balance will be
−$93.
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✔ Final Answers Summary:
1)
−40°F (temperature decrease)
2)
+51°F (temperature increase)
3)
78 (final score)
4)
$32 (initial amount)
5)
−$93 (new bank balance)
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✔ All problems involve
addition and subtraction of integers, and we’ve used appropriate signs to represent gains and losses.
Let me know if you'd like this formatted for printing or want explanations simplified further!
Parent Tip: Review the logic above to help your child master the concept of dividing integers word problems worksheet.
