Here are the answers to each question:
Question 1:
A recipe requires 3 cups of flour for every 2 cups of sugar. To find out how many cups of flour are needed for 8 cups of sugar, you can set up the proportion:
\[\frac{3 \text{ cups of flour}}{2 \text{ cups of sugar}} = \frac{x \text{ cups of flour}}{8 \text{ cups of sugar}}\]
Cross-multiply and solve for \(x\):
\[3 \cdot 8 = 2 \cdot x\] \[24 = 2x\] \[x = 12\]
Answer: 12
Question 2:
We have the proportional relationship where \(y = 5\) when \(x = 2\). We can find the constant of proportionality \(k\):
\[k = \frac{y}{x} = \frac{5}{2}\]
Now, we want to find \(y\) when \(x = 6\):
\[y = k \cdot x = \frac{5}{2} \cdot 6 = 15\]
Answer: 15
Question 3:
We know that \(y\) is directly proportional to \(x\) with \(y = 12\) when \(x = 4\). Find the constant of proportionality \(k\):
\[k = \frac{y}{x} = \frac{12}{4} = 3\]
Answer: 3
Question 4:
To solve the equation \(3x - 4 = 11\), we can add 4 to both sides:
\[3x = 15\]
Then, divide by 3:
\[x = 5\]
Answer: 5
Question 5:
To find \(x\) in the equation \(3x + 9 = 0\), we can subtract 9 from both sides:
\[3x = -9\]
Then, divide by 3:
\[x = -3\]
Answer: -3
In summary, the answers to your questions are:
- 12
- 15
- 3
- 5
- -3