Use the image to answer the question.

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

2 gallons
2 gallons

6 gallons
6 gallons

24 gallons
24 gallons

4 gallons

Answer 1

To solve for the amount of yellow paint Nate needs, we can start with the ratio of blue to yellow paint, which is 1:3.

This means that for every 1 part of blue paint, Nate needs 3 parts of yellow paint. The total parts in the mixture is:

1 (blue) + 3 (yellow) = 4 parts.

If Nate needs a total of 8 gallons of paint, we can set up the equation based on the total parts:

Let \( x \) be the amount of each part.

Since there are 4 parts total: \[ 4x = 8 \] Solving for \( x \): \[ x = \frac{8}{4} = 2 \text{ gallons} \]

Now, since the yellow paint makes up 3 parts of the total, we calculate the amount of yellow paint: \[ 3x = 3 \times 2 = 6 \text{ gallons} \]

Thus, Nate needs to buy 6 gallons of yellow paint.

The correct response is:

6 gallons