Class 7 Integers Word Problems | PDF - Free Printable

Let's solve each of these Class 7 integers word problems step by step.

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Question 1:

> In a school exam, Rohan’s score was up to 500 points. Then he scored -100 points in the words category. What was his score then?

Solution:

- Rohan's original score was 500 points.
- He scored -100 points in the words category (which means he lost 100 points).
- So, his final score = $ 500 + (-100) = 500 - 100 = 400 $

✔ Answer: Rohan’s score was 400 points.

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Question 2:

> Kamla has gone for a hiking trip. She ended a hike at an elevation of 5,000 feet above sea level. She had started at an elevation of 5,000 feet above sea level. Which integer represents Kamla’s change in elevation?

Solution:

- Starting elevation = 5,000 feet
- Ending elevation = 5,000 feet
- Change in elevation = Ending – Starting = $ 5000 - 5000 = 0 $

✔ Answer: The change in elevation is 0.

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Question 4:

> Tell whether the following statements are always true, sometimes true, or always false.

#### a. If a positive is subtracted from a negative integer, the difference is a negative integer.

Let’s analyze:
- Example: $ -5 - 3 = -8 $ → Negative
- Another: $ -2 - 1 = -3 $ → Negative
- Try: $ -1 - 100 = -101 $ → Still negative

But what if we think about it algebraically:
- Let $ a < 0 $ (negative), $ b > 0 $ (positive)
- Then $ a - b = \text{negative} - \text{positive} = \text{more negative} $
- So result is always negative.

✔ Answer: Always true

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#### b. If a positive integer is subtracted from a positive integer, the difference is a positive integer.

Check with examples:
- $ 10 - 3 = 7 $ → Positive ✔
- $ 5 - 10 = -5 $ → Negative ✘
- $ 8 - 8 = 0 $ → Not positive ✘

So, it depends on which number is larger.

✔ Answer: Sometimes true

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Question 5: Find solutions for the following problems:

#### a. Both numbers are less than 10. The distance between the two numbers on the number line is 14.

We need two numbers:
- Both < 10
- Distance between them = 14 → $ |x - y| = 14 $

Let’s suppose one number is $ x $, other is $ y $, and $ |x - y| = 14 $

Try possible values:
- Since both are less than 10, maximum value either can take is 9.
- But if one number is 9, the other must be $ 9 - 14 = -5 $ or $ 9 + 14 = 23 $ (but 23 > 10, invalid)

Try: $ x = -5 $, $ y = 9 $
- Are both < 10? Yes.
- Distance: $ |9 - (-5)| = |14| = 14 $ ✔

Other possibility: $ x = -6 $, $ y = 8 $? → $ |8 - (-6)| = 14 $ → also works.

But the question says "find solutions" — so any pair satisfying conditions.

✔ Answer: One possible solution: -5 and 9

(Or others like -6 and 8, -7 and 7, etc., as long as both < 10 and distance = 14)

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#### b. Both numbers are greater than -15 and less than 5. One number is 6 greater than the other number.

Let the smaller number be $ x $. Then the larger is $ x + 6 $

Conditions:
- $ x > -15 $
- $ x + 6 < 5 $ → $ x < -1 $
- Also $ x < 5 $, but already covered

So:
- $ x > -15 $
- $ x < -1 $

So $ x $ is between -15 and -1

Try $ x = -2 $ → $ x + 6 = 4 $
- Check: -2 > -15? Yes. 4 < 5? Yes. Difference = 6 ✔

Try $ x = -3 $ → $ x + 6 = 3 $ → valid

Try $ x = -10 $ → $ x + 6 = -4 $ → both within range ✔

Any such pair works.

✔ Answer: One possible solution: -2 and 4

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#### c. The numbers are opposites. The distance between the two numbers on the number line is 18.

Opposites mean: $ a $ and $ -a $

Distance = $ |a - (-a)| = |2a| = 18 $

So $ |2a| = 18 $ → $ |a| = 9 $ → $ a = 9 $ or $ a = -9 $

Then the numbers are: $ 9 $ and $ -9 $

✔ Answer: -9 and 9

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#### d. One number is -35. The distance between the two numbers on the number line is 20.

Let the other number be $ x $

Distance = $ |x - (-35)| = |x + 35| = 20 $

So:
- $ x + 35 = 20 $ → $ x = -15 $
- Or $ x + 35 = -20 $ → $ x = -55 $

So two possibilities:
- $ x = -15 $ → distance: $ |-15 + 35| = 20 $
- $ x = -55 $ → distance: $ |-55 + 35| = |-20| = 20 $

✔ Answer: The other number is either -15 or -55

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✔ Final Answers Summary:

#### Question 1:
Rohan’s score = 400

#### Question 2:
Change in elevation = 0

#### Question 4:
a. Always true
b. Sometimes true

#### Question 5:
a. Possible solution: -5 and 9
b. Possible solution: -2 and 4
c. -9 and 9
d. -15 or -55

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