Question
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)
Apologies for the mistake. Let's correct the solution.
According to the given ratio of 2:1 for blue paint to green paint, it means that for every 2 parts of blue paint, we need 1 part of green paint. Thus, the total number of parts is 2 + 1 = 3.
Since Angelina needs 6 gallons of paint, we can divide it into 3 equal parts, where each part represents a specific number of gallons.
Drawing a tape diagram, let's represent the parts as equal sections of the rectangle. Divide the rectangle into three sections, labeling them as "blue paint," "green paint," and "blue paint" again from left to right.
To determine the number of gallons per part, divide the total number of gallons (6) by the number of parts (3). So, each part represents 6/3 = 2 gallons.
Since Angelina wants to find out the number of gallons of blue paint she should buy, we need to determine the number of parts representing blue paint. As each part represents 2 gallons, Angelina needs 2 * 2 = 4 gallons of blue paint.
Hence, Angelina should buy 4 gallons of blue paint.
To solve this problem using a tape diagram, we can draw a rectangle divided into three parts representing the 2:1 ratio.
Using a pencil and ruler, draw a rectangle on a piece of paper. Divide the rectangle into three equal parts, and label the leftmost part as "blue paint," the middle part as "green paint," and the rightmost part as "blue paint" again.
Now, we know that for every 2 parts of blue paint, we need 1 part of green paint. Let's represent 1 part as a gallon, so each part of blue paint represents 2 gallons.
Since Angelina needs 6 gallons of paint in total, we can divide the rectangle into six equal parts, where each part represents one gallon.
Now, we need to find out how many gallons of blue paint Angelina should buy. Since each part of blue paint represents 2 gallons, we can count how many parts of blue paint are needed to get a total of 6 gallons.
Counting the parts, we can see that Angelina needs 3 parts of blue paint.
Therefore, Angelina should buy 3 gallons of blue paint.
that is wrong
To find out how many gallons of blue paint Angelina should buy, we need to use the ratio of 2:1 for blue to green paint. We can start by setting up the equation:
2x + x = 6
Where x represents the number of gallons of blue paint.
Now, we can solve for x:
3x = 6
Dividing both sides of the equation by 3:
x = 2
This means that Angelina should buy 2 gallons of blue paint.
A tape diagram can help organize the information visually. Here's how it would look:
Blue Paint : Green Paint
[ || || ]
Since the ratio is 2:1, we have two sections for blue paint and one section for green paint. In this case, each section represents one gallon of paint, and we need a total of 6 gallons. Therefore, we need 2 sections for blue paint, which is equivalent to 2 gallons.
To solve this problem, we can use a tape diagram, also known as a ratio diagram, to organize our thinking.
First, let's represent the ratio of blue to green paint as 2:1. We can draw a tape diagram with two sections for blue paint and one section for green paint.
Blue Blue Green
______ ______ ______
Now, we know that Angelina needs a total of 6 gallons of paint. Since the ratio of blue to green paint is 2:1, we can divide the tape diagram into equal parts.
Blue Blue Green
______ ______ ______
| | |
Next, we can assign a variable to represent the amount of paint in each section. Let's say each section represents x gallons.
Blue Blue Green
______ ______ ______
| x | x |
Since the ratio of blue to green paint is 2:1, the two blue sections combined should be twice the amount of the green section.
Therefore, we have the equation: 2x + 1x = 6
Simplifying the equation: 3x = 6
Dividing both sides of the equation by 3, we get: x = 2
So, each section represents 2 gallons of paint.
Now, to find out how many gallons of blue paint Angelina should buy, we can look at the blue sections. There are two blue sections, so she should buy 2 * 2 = 4 gallons of blue paint.
Therefore, Angelina should buy 4 gallons of blue paint.