Let's solve each question step by step:
Question 1: Solve for \( n \) in the equation \( \frac{n}{3} = 9 \).
Multiply both sides by 3: \[ n = 9 \times 3 = 27 \]
Answer: 27
Question 2: What is the equivalent form of \( 7(a+1) \)?
Distribute the 7: \[ 7(a+1) = 7a + 7 \]
Answer: 7a + 7
Question 3: A recipe requires a ratio of 2 cups of flour to 3 cups of sugar. If you have 6 cups of sugar, how many cups of flour do you need?
Set up the ratio: \[ \frac{2 \text{ cups flour}}{3 \text{ cups sugar}} = \frac{x \text{ cups flour}}{6 \text{ cups sugar}} \]
Cross-multiply to solve for \( x \): \[ 2 \times 6 = 3 \times x \implies 12 = 3x \implies x = \frac{12}{3} = 4 \]
Answer: 4 cups
Question 4: A car travels 180 miles in 3 hours. What is the car's speed in miles per hour?
Speed is calculated as distance divided by time: \[ \text{Speed} = \frac{180 \text{ miles}}{3 \text{ hours}} = 60 \text{ miles per hour} \]
Answer: 60 miles per hour
Question 5: The ratio of boys to girls in a class is 5:8. If there are 40 girls, how many boys are there?
Let \( b \) be the number of boys. The ratio can be expressed as: \[ \frac{b}{40} = \frac{5}{8} \]
Cross-multiply: \[ 8b = 5 \times 40 \implies 8b = 200 \implies b = \frac{200}{8} = 25 \]
Answer: 25 boys
Here are the final answers for each question:
- 27
- 7a + 7
- 4 cups
- 60 miles per hour
- 25 boys