Afamily went to the movies. tickets cost $4 for each child and $6 for each adult. the total admission charge for the family was $26. list all the possible numbers of adults and children in the family.

Let the number of children be x.

Cost for each child = $4,  total = 4*x = 4x

Let the number of adults be y.

Cost of each adult = $6, total = 6*y = 6y

Total = 4x + 6y = 26

4x + 6y = 26            Divide both sides by 2.

2x + 3y = 13

By inspection,  x could be 2, and y could be 3.

2x + 3y

2*2 + 3*3 = 4 + 9 = 13

So there could have been 2 children and 3 adults.

There could have also been 3 adults and 2 children

Hope this helps.