A class of 25 students has 10 boys. Three boys have braces and 4 girls have braces.
a) What is the ratio of boys with braces to boys in class?
b) What is the ratio of girls with braces to girls in class?
c) Which group has the largest ratio of students with braces to students in class--boys or girls?
ration 3:4
ratio 4:15
boys: 3:10 girls: 4:15
a) To find the ratio of boys with braces to boys in class, we need to divide the number of boys with braces (3) by the number of boys in class (10).
The ratio of boys with braces to boys in class is 3/10.
b) To find the ratio of girls with braces to girls in class, we need to divide the number of girls with braces (4) by the number of girls in class. However, we need to first calculate the number of girls in the class.
The total number of students in the class is 25. Since there are 10 boys, the number of girls can be found by subtracting the number of boys from the total number of students:
25 - 10 = 15
Now, we can calculate the ratio of girls with braces to girls in class by dividing the number of girls with braces (4) by the number of girls in class (15).
The ratio of girls with braces to girls in class is 4/15.
c) To determine which group has the largest ratio of students with braces to students in class, we compare the ratios of boys with braces to boys in class and girls with braces to girls in class.
The ratio of boys with braces to boys in class is 3/10, and the ratio of girls with braces to girls in class is 4/15.
To compare these ratios, we can convert them to a common denominator. The common denominator for 10 and 15 is 30.
The ratio of boys with braces to boys in class becomes 9/30 (multiplied by 3/3 to get the denominator of 30) and the ratio of girls with braces to girls in class becomes 8/30 (multiplied by 2/2 to get the denominator of 30).
Now, we can see that the ratio of boys with braces to boys in class is larger than the ratio of girls with braces to girls in class. Therefore, the group with the largest ratio of students with braces to students in class is boys.
To answer the given questions, we need to first find the total number of boys and girls, and then calculate the ratios based on the given information.
a) The number of boys with braces is 3. The number of boys in the class is 10.
Therefore, the ratio of boys with braces to boys in class is 3:10.
b) The number of girls with braces is 4. To find the number of girls in the class, we need to subtract the number of boys (10) from the total number of students (25).
So, the number of girls in the class is 25 - 10 = 15.
Therefore, the ratio of girls with braces to girls in class is 4:15.
c) To determine which group has the largest ratio of students with braces to students in the class, we compare the ratios calculated in parts a and b.
In part a, the ratio of boys with braces to boys in class is 3:10.
In part b, the ratio of girls with braces to girls in class is 4:15.
To compare the ratios, we need to find a common denominator. Here, the least common multiple (LCM) of 10 and 15 is 30.
Multiplying the first ratio by 3/3 and the second ratio by 2/2, we get:
Boys with braces to students in class ratio: 9:30
Girls with braces to students in class ratio: 8:30
Comparing the ratios, we can see that 9:30 is larger than 8:30.
Therefore, the group with the largest ratio of students with braces to students in class is the boys.