Let's solve each question one by one.
Question 1: Solve for \( n \) in the equation \( \frac{n}{3} = 9 \).
To solve for \( n \), multiply both sides by 3: \[ n = 9 \times 3 = 27 \] Answer: 27
Question 2: What is the equivalent form of \( 7(a + 1) \)?
Using the distributive property: \[ 7(a + 1) = 7a + 7 \] 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 a proportion: \[ \frac{2 \text{ cups flour}}{3 \text{ cups sugar}} = \frac{x \text{ cups flour}}{6 \text{ cups sugar}} \] Cross-multiply: \[ 2 \times 6 = 3 \times x \implies 12 = 3x \implies x = \frac{12}{3} = 4 \] 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?
Setting up the ratio: \[ \frac{5 \text{ boys}}{8 \text{ girls}} = \frac{x \text{ boys}}{40 \text{ girls}} \] Cross-multiply: \[ 5 \times 40 = 8 \times x \implies 200 = 8x \implies x = \frac{200}{8} = 25 \] Answer: 25 boys
Hereβs a summary of the answers:
- 27
- 7a + 7
- 4 cups
- 60 miles per hour
- 25 boys