1. **Problem 1:** Find the ratio of red cars to blue cars given the ratios red:green = 5:6 and green:blue = 3:10. Step 1: Write the given ratios: - Red : Green = 5 : 6 - Green : Blue = 3 : 10 Step 2: To find Red : Blue, we need to express the ratios with the same green term. Step 3: Find the least common multiple (LCM) of the green parts 6 and 3, which is 6. Step 4: Adjust the ratios: - Red : Green = 5 : 6 (already with green = 6) - Green : Blue = 3 : 10 → multiply both terms by 2 to get 6 : 20 Step 5: Now, Red : Green : Blue = 5 : 6 : 20 Step 6: Therefore, Red : Blue = 5 : 20 = 1 : 4 --- 2. **Problem 2:** When $a$ is multiplied by 1.75 it becomes $b$. Express $a:b$ in simplest form. Step 1: Given $b = 1.75a$ Step 2: The ratio $a:b = a : 1.75a$ Step 3: Divide both terms by $a$ (assuming $a \neq 0$): $$a:b = 1 : 1.75$$ Step 4: Convert 1.75 to fraction: $1.75 = \frac{7}{4}$ Step 5: So, $$a:b = 1 : \frac{7}{4} = \frac{4}{4} : \frac{7}{4} = 4 : 7$$ --- 3. **Problem 3:** $540$ is divided among three brothers in the ratio $\frac{3}{4} : \frac{2}{3} : \frac{5}{6}$. Find the amount each receives. Step 1: Write the ratio terms: $$\frac{3}{4}, \frac{2}{3}, \frac{5}{6}$$ Step 2: Find the least common denominator (LCD) of 4, 3, and 6, which is 12. Step 3: Convert each ratio term to have denominator 12: $$\frac{3}{4} = \frac{9}{12}, \quad \frac{2}{3} = \frac{8}{12}, \quad \frac{5}{6} = \frac{10}{12}$$ Step 4: The ratio is now $9 : 8 : 10$ Step 5: Sum of ratio parts: $$9 + 8 + 10 = 27$$ Step 6: Each part value: $$\frac{540}{27} = 20$$ Step 7: Amounts received: - Brother 1: $9 \times 20 = 180$ - Brother 2: $8 \times 20 = 160$ - Brother 3: $10 \times 20 = 200$ --- 4. **Problem 4:** A man left a legacy of 9450 to be divided among four daughters in the ratio 6:7:8:9. Find the amount each daughter receives. Step 1: Sum of ratio parts: $$6 + 7 + 8 + 9 = 30$$ Step 2: Each part value: $$\frac{9450}{30} = 315$$ Step 3: Amounts received: - Daughter 1: $6 \times 315 = 1890$ - Daughter 2: $7 \times 315 = 2205$ - Daughter 3: $8 \times 315 = 2520$ - Daughter 4: $9 \times 315 = 2835$