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
Based on the given ratio of 2:1 for blue to green paint, we can set up a proportion to determine the amount of blue paint needed.
Let x represent the number of gallons of blue paint needed.
Therefore, the amount of green paint needed would be (1/2)x gallons.
Since the total amount of paint needed is 6 gallons, we can set up the following equation:
x + (1/2)x = 6
To combine the like terms, we can multiply 1/2 by x, resulting in:
(3/2)x = 6
To isolate x, we can divide both sides of the equation by 3/2:
(3/2)x / (3/2) = 6 / (3/2)
Simplifying, we get:
x = 4
Thus, Angelina should buy 4 gallons of blue paint.
Methane gas contains carbon atoms and hydrogen atoms in the ratio of 1:4. A sample of methane gas contains 90 atoms. What value should be inserted into each rectangle? (1 point) The number should be inserted into each rectangle
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To solve this problem, we can use a tape diagram to help organize our thinking. Let's represent the total amount of paint needed as 6 gallons.
Since Angelina is mixing blue and green paint in a ratio of 2:1, we can divide the tape diagram into three equal parts:
Blue paint | Blue paint | Green paint
Since the ratio for blue paint is 2:1, we can divide the first two parts of the tape diagram into two equal parts each:
Blue paint | Blue paint | Green paint
Each of the blue paint parts represents one portion of blue paint. Since the total number of portions is 2, we need to find how many gallons of blue paint are in one portion.
To find the amount of blue paint needed, we can set up the following proportion:
2 portions / (2 portions + 1 portion) = x gallons / 6 gallons
2/3 = x/6
Cross-multiplying:
3x = 12
Dividing both sides of the equation by 3:
x = 4
Therefore, Angelina should buy 4 gallons of blue paint.
To find out how many gallons of blue paint Angelina should buy, we need to determine the ratio of blue paint to the total amount of paint.
Let's start by representing the ratio of blue paint to the total amount of paint using a tape diagram.
In the tape diagram, let's use B to represent gallons of blue paint and G to represent gallons of green paint.
The given ratio is 2:1 for blue paint to green paint. This means that for every 2 gallons of blue paint, Angelina needs 1 gallon of green paint.
Let's divide the tape diagram into 3 equal parts to represent the total amount of paint needed, which is 6 gallons.
| | |
B | | |
| | |
G | |
| |
Based on the ratio, we can allocate 2 equal parts to blue paint and 1 equal part to green paint.
| | |
B | B | |
| | |
G | |
| |
Now, we can see that we need a total of 3 equal parts of paint. Since each equal part represents 2 gallons of blue paint, Angelina would need 2 * 3 = 6 gallons of blue paint.
Therefore, Angelina should buy 6 gallons of blue paint.