Write the ratio of the mass of the stone to the mass of the dog.

Here are the solutions to the problems: r) Step 1: Write the ratio of the mass of the stone to the mass of the dog. Ratio = Mass of stone : Mass of dog Ratio = 30 kg : 90 kg Step 2: Simplify the ratio by dividing both sides by their greatest common divisor, which is 30. (30)/(30) : (90)/(30) 1 : 3 The ratio is 1:3. s) Step 1: Find the total number of parts in the ratio. 4 + 5 = 9 parts Step 2: Find the value of one part. (720)/(9 parts) = 80 per part Step 3: Calculate each share. First share: 4 × 80 = 320 Second share: 5 × 80 = 400 The shares are 320 and 400. Problem 2 (i) Step 1: Convert the mixed number to an improper fraction. 1 (1)/(2) = (3)/(2) Step 2: Write the proportion. q : (3)/(2) = 20 : 30 Step 3: Express the proportion as a fraction. (q)/(3)2 = (20)/(30) Step 4: Simplify the right side of the equation. (q)/(3)2 = (2)/(3) Step 5: Multiply both sides by (3)/(2) to solve for q. q = (2)/(3) × (3)/(2) q = 1 The value of q is 1. (ii) Step 1: Write the proportion. (3)/(4) : (1)/(2) = W : 16 Step 2: Express the proportion as a fraction. (3)/(4)(1)/(2) = (W)/(16) Step 3: Simplify the left side of the equation. (3)/(4) ÷ (1)/(2) = (3)/(4) × (2)/(1) = (6)/(4) = (3)/(2) So, the equation becomes: (3)/(2) = (W)/(16) Step 4: Multiply both sides by 16 to solve for W. W = (3)/(2) × 16 W = 3 × 8 W = 24 The value of W is 24. (iii) Step 1: Write the proportion as a fraction. (a)/(a+3) = (5)/(6) Step 2: Cross-multiply. 6 × a = 5 × (a+3) 6a = 5a + 15 Step 3: Subtract 5a from both sides. 6a - 5a = 15 a = 15 The value of a is 15. (iv) Step 1: Write the expenditure of Asha and Mbaga. Asha's expenditure = sh. 24000 Mbaga's expenditure = sh. 12000 Step 2: Form the ratio of their expenditure (Asha : Mbaga). 24000 : 12000 Step 3: Simplify the ratio by dividing both sides by their greatest common divisor, which is 12000. (24000)/(12000) : (12000)/(12000) 2 : 1 The ratio of their expenditure is 2:1. (v) Step 1: Convert the decimal and fraction to simpler forms. 0.5 = (1)/(2) (15)/(30) = (1)/(2) Step 2: Write the proportion with the simplified terms. (1)/(2) : (1)/(2) = 60 : B Step 3: Since the ratio on the left side is 1:1, the ratio on the right side must also be 1:1. 1 : 1 = 60 : B Step 4: This means B must be equal to 60. B = 60 The value of B is 60. (vi) Step 1: Find the total number of parts in the ratio. 2 + 3 + 5 = 10 parts Step 2: Find the value of one part. 1870 kg10 parts = 187 kg per part Step 3: Calculate each share. First share: 2 × 187 kg = 374 kg Second share: 3 × 187 kg = 561 kg Third share: 5 × 187 kg = 935 kg The shares are 374 kg, 561 kg, and 935 kg.