Draw and use a tape diagram to model and solve the problem below.
In a soccer league, the ratio of boys to girls is 4 to 6. There are a total of 50 players in the soccer league. Determine how many girls play in the soccer league.
A. 10
B. 20
C. 50
D. 30
it is 30
b/g = 2/3
or b = (2/3)g
b+g=50
2g/3 + 3g/3 = 50
5g/3 = 50
g = 150/5
To draw a tape diagram, we will represent the ratio of boys to girls, which is 4 to 6.
First, we will represent the ratio in terms of units. Since 4 + 6 = 10 (the total number of units in the ratio), we can say that each unit represents 50/10 = 5 players.
Next, we will draw a rectangle to represent the total number of players in the soccer league, which is 50. We will divide this rectangle into 10 equal parts (representing the total number of units in the ratio).
Now, we can use the tape diagram to determine the number of girls playing in the soccer league. Since the ratio of boys to girls is 4 to 6, we know that for every 4 units that represent boys, there are 6 units that represent girls.
To find the number of units representing girls, we multiply the total number of units (10) by the fraction of units representing girls (6/10):
Number of girls = 10 * (6/10) = 6.
Therefore, there are 6 girls playing in the soccer league.
Answer: D. 30
To solve this problem using a tape diagram, we first need to understand what it represents.
A tape diagram, also known as a bar model or fraction strip, is a way to visually represent and solve ratio and proportion problems. It involves dividing a whole into parts to represent different quantities.
In this problem, the ratio of boys to girls is 4 to 6. This means for every 4 boys, there are 6 girls.
To create a tape diagram, draw a bar divided into two parts: one representing boys and the other representing girls. Since the ratio is 4 to 6, divide the bar into 4 equal parts for boys and 6 equal parts for girls.
Now, we know that there are a total of 50 players in the soccer league. We can use the tape diagram to determine the number of girls.
Since the tape diagram represents the ratio of boys to girls as 4 to 6, we can think of each part representing a certain number of players.
Let's assign a value to each part. Since there are 50 players in total, each part will represent 50 divided by the sum of the parts (4 + 6).
The value of each part is:
50 / (4 + 6) = 50 / 10 = 5
Now, we can determine the number of girls by multiplying the value of each part representing girls by the number of parts for girls.
6 parts (representing girls) * 5 (the value of each part) = 30
Therefore, the correct answer is D. 30 girls play in the soccer league.