Use the image to answer the question.
An illustration shows a rectangle labeled as Blue. Another set of three adjacent rectangles is labeled as Yellow and is placed below Blue. All rectangles have the same dimensions. A bracket on the right side encompasses both sets and points to the number 8.
Nate is helping to redesign his basement. He is in charge of choosing and buying the paint. He wants a specific shade of green, so he is going to combine blue and yellow paint in the ratio of 1:3 . If he needs 8 gallons of paint, how much yellow paint does he need to buy?
(1 point)
Responses
4 gallons
4 gallons
24 gallons
24 gallons
2 gallons
2 gallons
6 gallons
6 gallons
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The answer is 6 gallons. Since the ratio of blue to yellow paint is 1:3, and Nate needs a total of 8 gallons of paint, we can set up the equation:
1x + 3x = 8
Combining like terms, we get:
4x = 8
Dividing both sides by 4, we find:
x = 2
Therefore, Nate needs to buy 3 times the amount of yellow paint, which is 3 * 2 = 6 gallons.
Based on the image, the bracket that encompasses both the Blue rectangle and the three adjacent Yellow rectangles points to the number 8. This indicates that the total amount of paint Nate needs is 8 gallons.
Since he wants to combine blue and yellow paint in a ratio of 1:3, he needs to determine how much yellow paint he requires.
To calculate this, he can set up the following equation:
1 part blue paint + 3 parts yellow paint = 8 gallons
Since the question asks for the amount of yellow paint needed, we can solve for that variable:
3 parts yellow paint = 8 gallons - 1 part blue paint
3 parts yellow paint = 8 gallons - 1 gallon
Therefore, Nate needs to buy 7 gallons of yellow paint to achieve the desired ratio of 1:3.
To answer this question, let's analyze the information provided in the image.
We can see that the blue rectangle represents 1 part of the mixture, and the three yellow rectangles represent 3 parts of the mixture. The total number of parts in the mixture is 4 (1 + 3).
We are given in the question that Nate needs 8 gallons of paint. Since the total number of parts in the mixture is 4, we can set up a proportion to determine how much yellow paint Nate needs to buy.
Proportion: (Amount of yellow paint) / (Total number of parts) = (Amount of paint needed) / (Total number of parts in the mixture)
From the image, we can see that the total number of parts is 4, and the amount of paint needed is 8 gallons.
Substituting the values into the proportion, we have:
(Amount of yellow paint) / 4 = 8 / 4
Simplifying the right side of the equation, we get:
(Amount of yellow paint) / 4 = 2
To solve for the amount of yellow paint, we can multiply both sides of the equation by 4:
(Amount of yellow paint) = 2 * 4
Therefore, the amount of yellow paint that Nate needs to buy is:
(Amount of yellow paint) = 8 gallons.
So the correct answer is 8 gallons.