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 initial score is 500 points.
- He scored -100 points in the words category. This means he lost 100 points.
- So, final score = Initial score + (-100)
= 500 + (-100)
= 400

✔ Answer: Rohan's final 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
= 5,000 – 5,000 = 0

✔ Answer: The change in elevation is 0 (no change).

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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
- Example: $-2 - 1 = -3$ → Negative
- In general: Negative − Positive = More negative → Always negative

✔ Answer: Always true

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

Check with examples:
- $10 - 3 = 7$ → Positive ✔
- $3 - 10 = -7$ → Negative ✘
- So it depends on which number is larger.

✔ Answer: Sometimes true

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Question 5: Find solutions for the following problems

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#### 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 = 14 → $|x - y| = 14$

Let’s suppose one number is $x$, other is $y$. Without loss of generality, assume $x > y$, so $x - y = 14$

But both numbers must be less than 10.

So maximum possible value of $x$ is just under 10, say 9.9, but since we’re dealing with integers, max is 9.

Then $x = 9$, $y = 9 - 14 = -5$

Check: Are both less than 10? Yes: 9 and -5 are both < 10
Distance = $|9 - (-5)| = |14| = 14$ ✔

Try another pair: $x = 8$, $y = -6$: $|8 - (-6)| = 14$ → Also valid

So many pairs exist.

✔ Answer: Possible pairs include: $(-5, 9)$, $(-6, 8)$, $(-7, 7)$, etc.

But let’s find all integer pairs where both numbers < 10 and distance = 14.

Let $x$ and $y$ be integers, $x > y$, $x - y = 14$, $x < 10$

Then $x < 10$, so $x \leq 9$

Then $y = x - 14 \leq 9 - 14 = -5$

So $y \leq -5$

So all such pairs: $x = 9, y = -5$; $x = 8, y = -6$; ... down to $x = 14, y = 0$ — but wait, $x < 10$, so $x \leq 9$

So $x = 9$ → $y = -5$
$x = 8$ → $y = -6$
...
$x = -5$ → $y = -19$ — still valid as long as both < 10

But there are infinitely many if we allow any integers.

But likely the question wants integer solutions with both numbers less than 10.

So:

- $x = 9, y = -5$
- $x = 8, y = -6$
- ...
- $x = 0, y = -14$
- $x = -1, y = -15$, etc.

But perhaps they want two numbers, so one possible answer is:

✔ Answer: One possible solution: 9 and -5

(Other valid answers exist.)

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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 two numbers be $x$ and $y$, with $x = y + 6$

Constraints:
- $-15 < x < 5$
- $-15 < y < 5$

Since $x = y + 6$, substitute into inequalities:

From $x < 5$:
$y + 6 < 5$ → $y < -1$

From $x > -15$:
$y + 6 > -15$ → $y > -21$

But also $y > -15$ (from original)

So combining: $-15 < y < -1$

And $y$ is integer (assume), so possible values: $y = -14, -13, ..., -2$

Then $x = y + 6$:
If $y = -14$, $x = -8$
If $y = -13$, $x = -7$
...
If $y = -2$, $x = 4$

Now check: Is $x < 5$? Yes, $x = 4$ is okay
Is $x > -15$? Yes

So all these work.

One example: $y = -2$, $x = 4$

Check:
- Both between -15 and 5? Yes
- Difference: $4 - (-2) = 6$ → Yes

✔ 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: $x$ and $-x$

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

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

So the numbers are $9$ and $-9$

✔ Answer: The numbers are 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:
- $x + 35 = 20$ → $x = -15$
- $x + 35 = -20$ → $x = -55$

So two possible solutions: $-15$ or $-55$

✔ 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. Example: 9 and -5 (any pair like this with difference 14, both < 10)
b. Example: -2 and 4
c. 9 and -9
d. -15 or -55

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