Erika gave 2 pencils to every girl and 3 pencils to every boy in her class. There were 5 more girls than boys in the class. She gave away 24 more pencils to the boys than the girls.
- How many children were there in the class?
- How many pencils were there altogether?
(a)
There were 5 more girls than boys.
If we remove the 5 extra girls, the number of girls and boys will be the same.
The difference in the number of pencils given between the girls and boys will increase.
Increase in the difference of the number of pencils if there were 5 less girls
= 5 x 2
= 10
Total difference in the number of pencils between the girls and the boys
= 24 + 10
= 34
Number of more pencils given to each girl than each boy
= 3 - 2
= 1
Number of sets of 1 girl and 1 boy
= 34 ÷ 1
= 34
Number of boys = 34
Number of girls
= 34 + 5
= 39
Number of children
= 34 + 39
= 73
(b)
Total number of pencils
= 34 x 3 + 39 x 2
= 102 + 78
= 180
Answer(s): (a) 73; (b) 180
