Angelina is painting her room. She wants a very specific shade of bright blue paint, so she mixes blue and green paint in a ratio of 2:1 . If she needs 6 gallons of paint, how many gallons of blue paint should she buy? Use a tape diagram to help organize your thinking.(1 point)
Blank gallons
To determine how many gallons of blue paint Angelina should buy, we can use a tape diagram.
Let's assume that the ratio of blue paint to green paint is represented by two blue boxes and one green box.
So, we have a total of three boxes in our tape diagram.
Since Angelina needs a total of 6 gallons of paint, we can divide the total into three equal parts.
Each part represents 6/3 = 2 gallons of paint.
Since the blue paint is represented by two blue boxes, Angelina should buy 2 * 2 = <<2*2=4>>4 gallons of blue paint.
Therefore, Angelina should buy 4 gallons of blue paint.
To find out how many gallons of blue paint Angelina should buy, let's first represent the ratio of blue to green paint using a tape diagram.
Let's represent blue paint with the letter 'B' and green paint with the letter 'G'. The ratio of blue to green paint is 2:1, which means for every 2 units of blue paint, there is 1 unit of green paint.
Start by drawing a rectangle to represent the total amount of paint Angelina needs, which is 6 gallons. Divide the rectangle into three parts, representing the blue paint, the green paint, and the total.
```
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| | | |
| B | G | T |
| | | |
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```
Now, since the ratio of blue to green paint is 2:1, divide the blue part into two equal parts and the green part into one part.
```
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| B | B | G | T |
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```
Each part represents one gallon of paint. So, we have 2 gallons of blue paint and 1 gallon of green paint.
Now, since Angelina needs a total of 6 gallons of paint, we can set up a proportion to solve for the number of gallons of blue paint.
2/3 = x/6
To solve for x, we cross-multiply and solve for x:
2 * 6 = 3 * x
12 = 3x
Divide both sides of the equation by 3:
12/3 = x
4 = x
Therefore, Angelina should buy 4 gallons of blue paint.
Let's represent the unknown amount of blue paint with a variable, say x.
According to the given ratio, the amount of green paint is 2 units.
To find the total number of units, we need to add the amount of blue paint and green paint, which is 2 + 1 = 3 units.
Now we can set up a proportion to find the value of x:
blue paint units / total units = blue paint gallons / total gallons
x / 3 = blue paint gallons / 6
To solve for x, we can cross-multiply and solve the equation:
6x = 3 * 6
6x = 18
x = 18 / 6
x = 3
Therefore, Angelina should buy 3 gallons of blue paint.