SOLUTION: There were 44 boys and 47 girls in a camp. The boys and girls were divided into groups. Each group has an equal number of pupils. The number of groups is larger than the number of

Question 908949: There were 44 boys and 47 girls in a camp. The boys and girls were divided into groups. Each group has an equal number of pupils. The number of groups is larger than the number of pupils in each group. How many groups were there?
All groups consist of some boys and girls. In each group, the number of boys is either 1 more or 1 less of the girls. How many groups had more girls than boys?
Answer by JulietG(1812) (Show Source): You can put this solution on YOUR website!
The total number of children in the camp is 44 + 47 = 91
If each group has an equal number of pupils, then the number of groups must be divisible by 91.
What are the factors of 91? 1,91,7,13
It's obviously not 1 and 91. Since the number of groups is larger, the number is 13 groups.
Therefore, there are 7 pupils in each group. 5 groups will have more boys and 8 groups will have more girls (there is a difference of 3 in the # of boys/girls)
Groups 1,2,3,4,5,6,7,8 = 4 girls + 3 boys (32 girls + 24 boys)
Groups 9,10,11,12,13 = 4 boys + 3 girls (20 boys + 15 girls)
Total: 24+20 boys (44); 32+15 girls (47)
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