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)
To find out how many gallons of blue paint Angelina should buy, we need to calculate the ratio of blue paint to the total amount of paint.
In this case, the ratio of blue paint to total paint is 2:3 (2 parts blue paint and 1 part green paint).
Since Angelina needs 6 gallons of paint in total, we can set up a proportion to solve for the amount of blue paint:
2 parts blue paint / 3 parts total paint = x gallons blue paint / 6 gallons total paint
Cross multiplying, we get:
2 * 6 = 3 * x
12 = 3x
Dividing both sides by 3, we can find x:
12 / 3 = x
4 = x
So, Angelina should buy 4 gallons of blue paint.
To find out how many gallons of blue paint Angelina should buy, let's use a tape diagram to help with the calculation.
A tape diagram is a visual representation of a problem using rectangles to represent quantities. In this case, we'll represent the blue and green paints using rectangles.
Let's assume we need x gallons of blue paint. Since Angelina wants to mix blue and green paint in a ratio of 2:1, she would need 2x gallons of green paint.
So, the tape diagram would look like this:
[ blue paint rectangle ] : x
[ green paint rectangle ] : 2x
According to the problem, she needs a total of 6 gallons of paint. Therefore, the blue and green paint should add up to 6 gallons.
So, our tape diagram now looks like this:
[ blue paint rectangle ] : x
[ green paint rectangle ] : 2x
Total: 6 gallons
To find x, we need to solve the equation x + 2x = 6.
Combining like terms, we get 3x = 6.
Dividing both sides of the equation by 3, we find that x = 2.
Therefore, Angelina should buy 2 gallons of blue paint.
Using the tape diagram helped us visualize the problem and set up the equation to solve for the unknown quantity.
To solve this problem, we can use a tape diagram to represent the ratio between blue and green paint.
Let's start by representing the total amount of paint needed, which is 6 gallons. We can draw a tape diagram with six sections:
[ ] [ ] [ ] [ ] [ ] [ ]
Now, we know that the ratio of blue to green paint is 2:1. This means that for every 2 units of blue paint, there is 1 unit of green paint. Let's represent this in the tape diagram:
[ ] [ ] [ ] [ ] [ ] [ ]
B B G B B G
We can see that each pair of blue and green paints represents 3 units of paint total (2 blue + 1 green). So, to fill the entire diagram, we need to have 3 pairs of blue and green paints. This equals a total of 9 units of paint (3 x 3).
Therefore, Angelina needs to buy 9 gallons of blue paint.