Anna gave 3 marbles to every boy and 6 marbles to every girl in her class. There were 5 more boys than girls in the class. She gave away 36 more marbles to the girls than the boys.
- How many children were there in the class?
- How many marbles were there altogether?
(a)
There were 5 more boys than girls.
If we remove the 5 extra boys, the number of boys and girls will be the same.
The difference in the number of marbles given between the boys and girls will increase.
Increase in the difference of the number of marbles if there were 5 less boys
= 5 x 3
= 15
Total difference in the number of marbles between the boys and the girls
= 36 + 15
= 51
Number of more marbles given to each boy than each girl
= 6 - 3
= 3
Number of sets of 1 boy and 1 girl
= 51 ÷ 3
= 17
Number of girls = 17
Number of boys
= 17 + 5
= 22
Number of children
= 17 + 22
= 39
(b)
Total number of marbles
= 17 x 6 + 22 x 3
= 102 + 66
= 168
Answer(s): (a) 39; (b) 168
