Hazel gave 2 cards to every boy and 3 cards to every girl in her class. There were 7 more boys than girls in the class. She gave away 15 more cards to the girls than the boys.
- How many children were there in the class?
- How many cards were there altogether?
(a)
There were 7 more boys than girls.
If we remove the 7 extra boys, the number of boys and girls will be the same.
The difference in the number of cards given between the boys and girls will increase.
Increase in the difference of the number of cards if there were 7 less boys
= 7 x 2
= 14
Total difference in the number of cards between the boys and the girls
= 15 + 14
= 29
Number of more cards given to each boy than each girl
= 3 - 2
= 1
Number of sets of 1 boy and 1 girl
= 29 ÷ 1
= 29
Number of girls = 29
Number of boys
= 29 + 7
= 36
Number of children
= 29 + 36
= 65
(b)
Total number of cards
= 29 x 3 + 36 x 2
= 87 + 72
= 159
Answer(s): (a) 65; (b) 159
