The ratio of boys to girls is 3 to 7. If there are 200 more girls than boys, how many boys are there? Use a tape diagram to solve.
Given:
Girls : Boys = 7 : 3
Girls+Boys:Girls-Boys = 10:4 = X:200
where X is the total number of children (Girls+Boys)
or
10/4=X/200
Cross multiply to find
X=200*10/4 = 500
To solve this problem using a tape diagram, we can start by drawing two rectangles, one for boys and one for girls. We'll label the rectangle for boys as "B" and the rectangle for girls as "G."
Now, we know the ratio of boys to girls is 3 to 7. This means, for every 3 parts representing boys, there are 7 parts representing girls. So, for the tape diagram, we'll divide the rectangles into 10 equal parts, with 3 parts for boys and 7 parts for girls.
Next, we're given that there are 200 more girls than boys. We can represent this on the tape diagram by adding 200 more units to the girls' rectangle.
Now, the difference between the total units in the girls' rectangle and the total units in the boys' rectangle is 200. Since the difference between the parts representing boys and girls is still 4 (7 parts - 3 parts), we can find the value of 4 by dividing 200 by the difference (200 / 4 = 50).
Therefore, the number of boys is 3 units per part multiplied by 50 parts, which equals 150 boys.