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.

Question

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

6 gallons
6 gallons

24 gallons
24 gallons

4 gallons
4 gallons

2 gallons
2 gallons
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Answer 1

To find out how much yellow paint Nate needs to buy, we start by looking at the ratio of blue to yellow paint, which is 1:3. This means for every 1 part blue, there are 3 parts yellow.

Let's denote the amount of blue paint Nate needs as \( B \) and the amount of yellow paint as \( Y \).

Since the ratio is 1:3, we can express it as: \[ B:Y = 1:3 \]

This means: \[ Y = 3 \times B \]

Nate wants a total of 8 gallons of paint, so: \[ B + Y = 8 \]

Substituting \( Y \) in the total paint equation: \[ B + 3B = 8 \] \[ 4B = 8 \] \[ B = 2 , \text{gallons} \]

Now, substituting back to find \( Y \): \[ Y = 3 \times B = 3 \times 2 = 6 , \text{gallons} \]

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

The correct response is: 6 gallons