There are 27 students in a class. The number of boys and the number of girls are both COMPOSITE numbers.?

Answer 1

Lots of choices:
6 boys and 21 girls
9 boys and 18 girls
12 boys and 15 girls
15 boys and 12 girls
18 boys and 9 girls
21 boys and 6 girls

Without another piece of information (such as there are 3 more girls than boys, or twice as many boys as girls) there is no way to get a unique answer.

Answer 2

6 and 21
9 and 18
12 and 15

The way to approach this is to first determine one-half of the number, rounding down if needed: 1/2 of 27 is 13.5, round down to 13.

Now look at each number from 4 (the first composite number) through the the value just calculated, and see if that number is composite -- if not move on to the next one. When you have a composite number, subtract that from 27 and see if the result is composite. If so, both are composite and their sum is the class size so this is a solution:

1, 2, 3: not composite
4: 27-4 = 23, which is not composite
5: not composite
6: 27-6 = 21, which is composite >>> SOLUTION 6 and 21
7: not composite
8: 27-8 = 19, which is not composite
9: 27-9 = 18, which is composite >>> SOLUTION 9 and 18
10: 27-10 = 17, which is not composite
11: not composite
12: 27-12 = 15, which is composite >>> SOULUTION 12 and 15
13: not composite

You don't need to go past 13, because after that you will just find the "reverse images" of the solutions (15 and 12, 18 and 9, 21 and 6). For a problem like this, these "reverse images" mean just flipping which number represents the boys and which one represents the girls -- so the solution of "12 and 15" means for example 12 boys and 15 girls, while the "reverse image" solution of "15 and 12" means 15 boys and 12 girls.

Answer 3

12 and 15

Answer 4

permit the variety of boys be b. permit the variety og women be g. b + g = 27 --- (a million) b + 3 = g --- (2) Substi. (2) into (a million). b + (b + 3) = 27 2b = 24 b = 12 Substi. b = 12 into (2). 12 + 3 = g g = 15 There are 15 women and 12 boys in the class.