A recipe requires 3 cups of flour for every 2 cups of sugar. How many cups of flour are needed for 8 cups of sugar?(1 point)

Question

Responses

9
9

10
10

12
12

16
16
Question 2
In a proportional relationship, if ( y = 5 ) when ( x = 2 ), what is the value of ( y ) when ( x = 6 )?
(1 point)
Responses

10
10

12.5
12.5

15
15

20
20
Question 3
If ( y ) is directly proportional to ( x ) and ( y = 12 ) when ( x = 4 ), what is the constant of proportionality?(1 point)
Responses

1
1

2
2

3
3

4
4
Question 4
What is the solution to the equation 3𝑥−4=11?(1 point)
Responses

6
6

5
5

3
3

2
2
Question 5
What is the value of 𝑥 in the equation 3𝑥+9=0?(1 point)
Responses

-1
-1

-2
-2

-3
-3

-4
-4
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Answer 1

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

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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

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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

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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

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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

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In summary, the answers to your questions are:

1. 12
2. 15
3. 3
4. 5
5. -3