Tape Diagrams Practice
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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.
$$ gallons
To solve this question, we can start by setting up a tape diagram to represent the ratio of blue to green paint.
Let's say that each unit on the tape diagram represents 1 gallon. We have 2 units for blue paint and 1 unit for green paint.
We know that Angelina needs a total of 6 gallons of paint. To find out how much blue paint she needs, we can set up a proportion:
2 units / 3 units = x gallons / 6 gallons
Cross multiplying, we get:
2 * 6 = 3 * x
12 = 3x
Therefore, x = 4
So, Angelina should buy 4 gallons of blue paint.
To solve this problem using a tape diagram, we can represent the ratio 2:1 as two parts of blue paint and one part of green paint.
Let's draw a tape diagram with two sections for blue paint and one section for green paint:
Blue Paint Blue Paint Green Paint
_________ _________ _________
Now, we know that Angelina needs a total of 6 gallons of paint. We can divide this total into three parts, representing the three sections of the tape diagram.
Since the ratio of blue paint to green paint is 2:1, we can divide the 6 gallons of paint into two parts of blue paint and one part of green paint.
Let's divide the tape diagram accordingly by labeling the sections:
Blue Paint Blue Paint Green Paint
_________ _________ _________
2 2 1
Now we can find the value of one part by dividing 6 gallons by the sum of the ratios, which is 2 + 1 = 3:
1 part = 6 gallons ÷ 3 = 2 gallons
Since one part represents 2 gallons of paint, we can multiply this value by the number of parts of blue paint needed, which is 2, to find the total amount of blue paint Angelina should buy:
Total blue paint = 2 parts × 2 gallons/part = 4 gallons
Therefore, Angelina should buy 4 gallons of blue paint.