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)
gallons and it's not 3 gallons
Let's represent the amount of blue paint with the variable "b" and the amount of green paint with the variable "g".
According to the ratio of 2:1, we can represent the amount of green paint as half of the amount of blue paint. So, g = (1/2)b.
The total amount of paint needed is 6 gallons, so we can write the equation: b + g = 6.
Substituting the value of g from the ratio equation, we get: b + (1/2)b = 6.
Combining like terms, we have: (3/2)b = 6.
To solve for b, we divide both sides of the equation by 3/2: b = (6 * 2)/3.
Simplifying the right side, we get: b = 12/3.
Therefore, Angelina should buy 4 gallons of blue paint.
To determine how many gallons of blue paint Angelina should buy, we can set up a ratio based on the given ratio of blue to green paint (2:1).
Let's use the variable "x" to represent the number of gallons of blue paint.
From the ratio, we can write the equation:
2/1 = x/6
To solve for x, we can cross-multiply and simplify:
2*6 = 1*x
12 = x
Therefore, Angelina should buy 12 gallons of blue paint.
To solve this problem, we can use a tape diagram to visualize the ratio of blue paint to green paint.
Let's start by representing the total amount of paint needed, which is 6 gallons, with a tape diagram. We can divide the tape into three equal parts to represent the total paint quantity.
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Next, we know that Angelina wants the ratio of blue paint to green paint to be 2:1. This means that for every three parts, two parts should be blue paint, and one part should be green paint.
Let's divide the tape into three equal parts and label them as blue and green paint.
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| Blue | Blue | Green |
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Now, we need to determine the quantity of each part. Since Angelina needs a total of 6 gallons of paint, we can divide the tape equally into 6 parts, where each part represents 1 gallon.
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| Blue | Blue | Green |
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1 1 1
From the tape diagram, we can see that Angelina needs 2 gallons of blue paint and 1 gallon of green paint.
Therefore, Angelina should buy 2 gallons of blue paint.