Question

A school has 225 students in the 7th grade period of the students, there are 126 boys and 99 girls. You want to create groups of students where each group has the same amount of boys and each group has the same amount of girls. Each group will have less girls the boys. How many groups should you create?

Answer 1

The greatest common divisor of 126 and 99 is 9, so we can form 9 groups with each group having 14 boys and 11 girls.

Step-by-step explanation:

To create groups from the 225 7th grade students — 126 boys and 99 girls — with each group having the same number of boys and girls, and with fewer girls than boys in each group, we need to find the greatest common divisor (gcd) of the number of boys and girls. The gcd for 126 and 99 is 9.

Therefore, to form the groups with the same number of boys and girls and to ensure each group has fewer girls than boys, we divide both numbers by the gcd. Dividing 126 by 9 gives us 14, and dividing 99 by 9 gives us 11. So, we can form 9 groups, with each group consisting of 14 boys and 11 girls.