Question
Use the table to answer the question.
White Red
3 4
blank 8
9 12
12 blank The ratio of red to white paint to make the perfect color pink is 4 tablespoons of red paint to 3 tablespoons of white paint. How many tablespoons of white paint are needed if there are 8 tablespoons of red paint? How many tablespoons of red paint are needed if there are 12 tablespoons of white paint?
wrong
Apologies for the mistake in my previous response. Let's reevaluate the situation.
According to the ratio of red to white paint for the perfect color pink being 4 tablespoons of red paint to 3 tablespoons of white paint, we can use this ratio to find out how many tablespoons of white paint are needed when there are 8 tablespoons of red paint.
Since the ratio is 4:3, we can set up the following proportion:
4/3 = 8/x
To solve for x, we can cross-multiply:
4x = 3 * 8
4x = 24
x = 24/4
x = 6
Therefore, if there are 8 tablespoons of red paint, we will need 6 tablespoons of white paint.
Now, let's determine the amount of red paint needed when there are 12 tablespoons of white paint.
Using the same ratio of 4:3, we can set up the following proportion:
4/3 = y/12
To solve for y, we can cross-multiply:
4 * 12 = 3y
48 = 3y
y = 48/3
y = 16
Therefore, if there are 12 tablespoons of white paint, we will need 16 tablespoons of red paint.
I apologize for any confusion caused by my earlier response.
12 and 16 are wrong
Apologies again for the earlier incorrect responses. Let's correct our calculations.
If there are 8 tablespoons of red paint, we can use the ratio 4:3 to find how many tablespoons of white paint are needed.
The ratio of red to white paint is 4:3, so we can set up the following proportion:
4/3 = 8/x
Cross-multiplying, we get:
4x = 3 * 8
4x = 24
x = 24/4
x = 6
Therefore, if there are 8 tablespoons of red paint, 6 tablespoons of white paint are needed.
For the second part, if there are 12 tablespoons of white paint, we can use the same ratio to find how many tablespoons of red paint are needed.
Setting up the proportion:
4/3 = y/12
Cross-multiplying:
4 * 12 = 3y
48 = 3y
Dividing both sides by 3:
16 = y
Therefore, if there are 12 tablespoons of white paint, 16 tablespoons of red paint are needed.
I apologize for the confusion caused by my earlier incorrect responses. Please let me know if there's anything else I can assist you with.
To answer these questions, we need to understand the given information from the table and then apply the ratio provided.
Let's analyze the table first:
White Red
3 4
blank 8
9 12
12 blank
From the table, we can observe that there are two scenarios mentioned:
1. When there are 8 tablespoons of red paint, and the corresponding value of white paint is blank.
2. When there are 12 tablespoons of white paint, and the corresponding value of red paint is blank.
Now, let's solve each scenario one by one:
Scenario 1: When there are 8 tablespoons of red paint (and white paint is blank):
According to the given ratio of red to white paint, the ratio is 4:3. This means that for every 4 tablespoons of red paint, we need 3 tablespoons of white paint.
We are given that there are 8 tablespoons of red paint. To find the corresponding amount of white paint, we can set up a proportion:
(4 tablespoons of red paint) / (3 tablespoons of white paint) = (8 tablespoons of red paint) / (x tablespoons of white paint)
To solve for x (the amount of white paint needed), we can cross multiply and solve the equation:
3 * (8 tablespoons of red paint) = 4 * (x tablespoons of white paint)
24 = 4x
Dividing both sides by 4:
x = 6
So, if there are 8 tablespoons of red paint, we need 6 tablespoons of white paint.
Scenario 2: When there are 12 tablespoons of white paint (and red paint is blank):
Using the same logic as before, we can set up a new proportion:
(4 tablespoons of red paint) / (3 tablespoons of white paint) = (x tablespoons of red paint) / (12 tablespoons of white paint)
Cross multiplying and solving the equation:
3 * (x tablespoons of red paint) = 4 * (12 tablespoons of white paint)
3x = 48
Dividing both sides by 3:
x = 16
So, if there are 12 tablespoons of white paint, we need 16 tablespoons of red paint.
In summary:
- If there are 8 tablespoons of red paint, we need 6 tablespoons of white paint.
- If there are 12 tablespoons of white paint, we need 16 tablespoons of red paint.
If there are 8 tablespoons of red paint, we can use the ratio 4:3 to find how many tablespoons of white paint are needed.
Since the ratio is 4 tablespoons of red paint to 3 tablespoons of white paint, we can set up the following proportion:
4/3 = 8/x
Cross-multiplying, we get:
4x = 3 * 8
4x = 24
x = 24/4
x = 6
Therefore, 6 tablespoons of white paint are needed if there are 8 tablespoons of red paint.
If there are 12 tablespoons of white paint, we can use the same ratio 4:3 to find how many tablespoons of red paint are needed.
We can set up the following proportion:
4/3 = y/12
Cross-multiplying, we get:
4 * 12 = 3y
48 = 3y
y = 48/3
y = 16
Therefore, 16 tablespoons of red paint are needed if there are 12 tablespoons of white paint.