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