Grades 11-12 Video Solutions 2011-11&12 Video Solutions 2011 problem13

Video Transcription

Question number 13. 48 boys went on a skiing trip. Six of them arrived with exactly one brother,  nine of them came with exactly two brothers, and four of them came with exactly three brothers.  The remaining boys were not accompanied by any siblings. How many families did these 48 boys represent?  Let's first focus on the boys that arrived with siblings and count how many families these boys represent. Six of them arrived with one brother, so that's two children per family.  Nine arrived with exactly two brothers, that's three children per family. And four with three brothers, that's four children per family.  And this gives us three plus three plus one, a total of seven families with multiple children.  So then we have to find out how many families have just one child that were on this skiing trip.  Now the 48 boys, we subtract exactly the ones we already counted, so six plus nine plus four gives us 48 minus 19, which is 29.  And each boy came from a family where he was the only child, so that's 29 families with just one child.  And so we have our total, 29 plus 7, or 36 families, which gives us the answer, D.

Video Summary

The problem involves determining the number of families represented by 48 boys on a skiing trip. Of these, 19 boys arrived with siblings, representing seven families: six boys with one brother (2 per family), nine boys with two brothers (3 per family), and four boys with three brothers (4 per family). The remaining 29 boys were the only children in their respective families. Adding these, the total is 36 families (29 single-child families + 7 multi-child families). The answer is 36 families.

Keywords

skiing trip

families

siblings

boys

single-child