Question

In a group of students, the ratio of girls to boys is 3 to 2. If there are 15 girls, how many total students are there?

Answer 1

To find the total number of students in a group where the ratio of girls to boys is 3:2 and there are 15 girls set up a proportion and solve for the number of boys. Finally, add the number of girls and boys to get the total number of students.

Step-by-step explanation:

To find the total number of students, we need to determine the total number of boys in the group. From the given ratio of girls to boys, which is 3:2, we can set up a proportion:

Girls / Boys = 3 / 2

Since we know that there are 15 girls, we can substitute this value into the proportion:

15 / Boys = 3 / 2

To solve for the number of boys (Boys), we can cross multiply and solve for Boys:

(15)(2) = (3)(Boys)

30 = 3Boys

Dividing both sides by 3, we get: Boys = 10

Therefore, the total number of students is the sum of the number of girls and the number of boys:

Total students = Girls + Boys = 15 + 10 = 25.

Answer 2

The ratio of girls to boys is 3:5, or three to five. This means that for every 5 boys, there are 3 girls in the class. We can think of the boys as being in "groups" of 5. For every group of 5 boys, there will be a group of 3 girls. How many groups of 5 boys are in the classroom? There are 15 boys, which means there are 3 groups of 5 (3 times 5 equals 15). Since there are 3 girls for every 5 boys, this means there are also 3 groups of girls, but there are 3 girls in each group instead of 5. 3 times 3 equals 9, so there are 9 girls. Total students equals 15 plus 9, or 24. Another way of thinking about this is by cross multiplying. 3/5 = g/15 (make sure you keep the boys and girls in the same order. Girls are in the numerator, boys are in the denominator for both). When you cross multiple, you get 3 * 15 = 5*g. Solve for g, and you get g = (3 * 15) / 5, or 45 / 5, or 9. Add 9 to the 15 boys for the total, and you get 24.