Answers

44. The sum of two integers is –1500. If one of them is 599, find the other.

Let the other number be x:

$$599 + x = -1500 \Rightarrow x = -1500 - 599 = \boxed{-2099}$$

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45. Find the value of $125 - 200 \div 8 + 5 \times 25$

Follow BODMAS/BIDMAS:

Step 1: $200 \div 8 = 25$
Step 2: $5 \times 25 = 125$
Now calculate:

$$125 - 25 + 125 = \boxed{225}$$

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46. Garvit earns a profit of ₹2 per pen, loss of ₹0.50 per pencil. He earns ₹10 total. Sold 15 pens. Find pencils?

Profit from 15 pens = $15 \times 2 = ₹30$
Let pencils sold = x

Loss from x pencils = $x \times 0.5 = 0.5x$
Net profit = ₹10

$$30 - 0.5x = 10 \Rightarrow 0.5x = 20 \Rightarrow x = \boxed{40 \text{ pencils}}$$

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47. Add additive inverse of $(-12 + 16 - 42 \div 3 + 3 \div 7)$ to product of $-2, -3, -4$

Step 1: Inside the expression

$$-12 + 16 = 4 42 \div 3 = 14 3 \div 7 = \frac{3}{7} \Rightarrow 4 - 14 + \frac{3}{7} = -10 + \frac{3}{7} = \frac{-70 + 3}{7} = \frac{-67}{7}$$

Additive inverse of that = $\boxed{\frac{67}{7}}$

Step 2: Product of –2, –3, –4

$$-2 \times -3 = 6,\quad 6 \times -4 = -24$$

Step 3: Add both

$$\frac{67}{7} + (-24) = \frac{67 - 168}{7} = \boxed{\frac{-101}{7}}$$

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48. From number line: Find additive inverse of (A – B – C)

From number line:
A = 2, B = –3, C = 4
Then:

$$A - B - C = 2 - (-3) - 4 = 2 + 3 - 4 = 1 \Rightarrow \text{Additive inverse of 1 is } \boxed{-1}$$

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49. Elevator starts from 5th floor

• Up 4 floors → 5 + 4 = 9

• Down 6 floors → 9 - 6 = 3

• Up 9 floors → 3 + 9 = 12

• Down 5 floors → 12 - 5 = \boxed{7th floor}

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50. Product of three integers = –900. Two are +25 and –6. Find third.

Let third = x

$$25 \times (-6) \times x = -900 \Rightarrow -150x = -900 \Rightarrow x = \boxed{6}$$

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