Question

Hector is dividing students into groups for an HR wants to divide the boys and girls so that each group has the same number of the boys and girls their 21 boys and 56 girls signed up for the hike to how many groups can the students be divided how many boys and how many girls will be in each group.​

Answer 1

7 groups, 3 boys and 8 girls

Explanation:

Let total number of groups be
`x`

and total hikers in one group be
`y`

if number of girls and boys in every group is same, then

`(21)/(x) + (56)/(x) = y`

`(21 + 56)/(x) = y\\x*y = 77` ....(1)

from (1)
`x` will either be 11 or 7

for
`x = 11` the values won't be real.

For
`x = 7\\y = (77)/(7) \\y = 11`

so there will be 7 groups with 11 hikers in each groups and every group will have
`(21)/(7) = 3` boys and
`(56)/(7) = 8` girls