Evaluate 4 1/2 ÷ 1 1/3 + 2 1/3 - 3/4

Here are the solutions to your problems:

1. Evaluate $4\frac{1}{2} \div 1\frac{1}{3} + 2\frac{1}{3} - \frac{3}{4}$

Step 1: Convert all mixed numbers to improper fractions. $4\frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{9}{2}$ $1\frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{4}{3}$ $2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$ The expression becomes: $\frac{9}{2} \div \frac{4}{3} + \frac{7}{3} - \frac{3}{4}$

Step 2: Perform the division. To divide by a fraction, multiply by its reciprocal. $\frac{9}{2} \div \frac{4}{3} = \frac{9}{2} \times \frac{3}{4} = \frac{27}{8}$ The expression becomes: $\frac{27}{8} + \frac{7}{3} - \frac{3}{4}$

Step 3: Find a common denominator for the fractions. The least common multiple of 8, 3, and 4 is 24. $\frac{27}{8} = \frac{27 \times 3}{8 \times 3} = \frac{81}{24}$ $\frac{7}{3} = \frac{7 \times 8}{3 \times 8} = \frac{56}{24}$ $\frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}$ The expression becomes: $\frac{81}{24} + \frac{56}{24} - \frac{18}{24}$

Step 4: Perform the addition and subtraction. $\frac{81 + 56 - 18}{24} = \frac{137 - 18}{24} = \frac{119}{24}$

Step 5: Convert the improper fraction to a mixed number. $\frac{119}{24} = 4 \frac{23}{24}$ The final answer is $\boxed{4\frac{23}{24}}$.

2. A shopkeeper bought 12 bags of maize at 185. He sold them at 225. Find his profits.

Step 1: Determine the total cost price (CP). Assuming "bought 12 bags of maize at 185" means the total cost for all 12 bags was 185. $\text{Total CP} = 185$

Step 2: Determine the total selling price (SP). Assuming "He sold them at 225" means he sold each bag for 225. $\text{Total SP} = 12 \text{ bags} \times 225/\text{bag} = 2700$

Step 3: Calculate the profit. $\text{Profit} = \text{Total SP} - \text{Total CP}$ $\text{Profit} = 2700 - 185 = 2515$ The final answer is $\boxed{2515}$.

3. Solve for $\alpha$: $3\alpha + 7 = 2\alpha + 19$

Step 1: Subtract $2\alpha$ from both sides of the equation to collect $\alpha$ terms on one side. $3\alpha - 2\alpha + 7 = 2\alpha - 2\alpha + 19$ $\alpha + 7 = 19$

Step 2: Subtract 7 from both sides of the equation to isolate $\alpha$. $\alpha + 7 - 7 = 19 - 7$ $\alpha = 12$ The final answer is $\boxed{12}$.

4. A car uses 8 litres of petrol to cover 100 km. How many litres will it cover 325 km?

Step 1: Determine the petrol consumption rate per kilometer. $\text{Consumption rate} = \frac{8 \text{ litres}}{100 \text{ km}} = 0.08 \text{ litres/km}$

Step 2: Calculate the total litres needed for 325 km. $\text{Litres needed} = \text{Consumption rate} \times \text{Distance}$ $\text{Litres needed} = 0.08 \text{ litres/km} \times 325 \text{ km}$ $\text{Litres needed} = 26 \text{ litres}$ The final answer is $\boxed{26 \text{ litres}}$.