Question

214 boys and 230 girls signed up to participate in The Amusing Race. Two days before the event, 4 boys and

6 girls withdrew from the event. 'The remaining boys and girls had to be equally divided into as many
groups as possible such that every group had the same number of boys and girls. Find
(i) the greatest number of groups that can be formed,
(in) the number of boys and the number of girls in each group.

Answer 1

(i) 14 groups

(in) 15 boys per group and 16 girls per group

Explanation:

(i) After the withdrawal of the 4 boys and 6 girls, there are 210 boys and 224 girls left. To find the greatest number of groups that can be formed with an equal number of boys in each group and an equal number of girls in each group, you need to find the GCF (Greatest Common Factor) of 210 and 224. Since 210 is 2 * 3 * 5 * 7 and 224 is 2^5 * 7 the GCF of these two numbers is what they have in common which is 2 * 7 which is 14. Thus, 14 is the greatest number of groups that can be formed.

(in) When 14 groups are formed, there are 210/14 boys in each group and 224/14 girls in each group. That results in 15 boys per group and 16 girls per group.

Hope this helps :)