A new superhero movie has its first showing and there are 155 people in line to see it. if the ratio of kids to adults waiting to see this movie is 3:2, how many adults are in line? Use a tape diagram to help organize your thinking.
To solve this problem using a tape diagram, we can break up the line into 5 equal parts, representing the 5 equal parts in the ratio 3:2.
Each part represents 155 ÷ 5 = 31 people.
Therefore, there are 31 x 2 = <<31*2=62>>62 adults in line. Answer: \boxed{62}.
To find the number of adults in line, we need to use the given ratio of kids to adults, which is 3:2.
1. Start by representing the ratio in a tape diagram. Draw two segments (or rectangles) to represent the parts for kids and adults.
____ ____ ____
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| 3 | | 2 |
|____| |____|
2. We know that the total number of segments on both sides of the tape diagram represents the total number of people in line, which is 155.
____ ____ ____
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| 3 | | 2 |
|____| |____|
So, we need to divide the total length of the tape diagram by 155 equally.
3. Divide the total length of the tape diagram into 5 equal parts (3 for kids + 2 for adults).
____ ____ ____
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|____| |____|
4. Determine the length of one equal part, which represents 1 person. Divide the length of one segment (kids or adults) by 5, and assign a value to it.
Length of one segment = total length / 5
Let's say the total length is 'L.'
Length of one segment = L / 5
We don't know the value of L, but we can represent it as 5x, where x is an unknown value.
Length of one segment = 5x / 5
Length of one segment = x
Now, we have the length of one segment as 'x'.
5. Multiply the length of one segment by the number of kids (3x) and adults (2x) to find their respective quantities.
Kids = 3x
Adults = 2x
6. We know the total number of people in line is 155. Set up an equation to find the value of 'x' and solve for it.
Kids + Adults = Total number of people
3x + 2x = 155
5x = 155
x = 155/5
x = 31
7. Substitute the value of 'x' back into the expressions for kids and adults.
Kids = 3x = 3 * 31 = 93
Adults = 2x = 2 * 31 = 62
Therefore, there are 62 adults in the line to see the superhero movie.