Forming Groups
Seventy pupils are divided into two groups. Can you work out the difference between the number of boys in group 1 and the number of girls in group 2?
Age
11 to 14
Challenge level
Problem
Seventy pupils (37 boys and 33 girls) are divided into two groups, with 40 pupils in Group 1 and 30 pupils in Group 2.
What is the difference between the number of boys in Group 1 and the number of girls in Group 2?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 7
Using expressions
Let the number of Boys in Group 1 be $x$.
The number of Girls in Group 1 is therefore $40-x$.
Therefore the number of Girls in Group 2 is $33 - (40 - x) = x - 7$.
There are therefore $7$ more Boys in Group 1 than Girls in Group 2.
Using an example
If all the Boys are in Group 1 there will be:
37 Boys and 3 Girls in Group 1
30 Girls in Group 2
If we swap one Boy from Group 1 with one Girl from Group 2 there will be:
36 Boys and 4 Girls in Group 1
29 Girls and 1 Boy in Group 2
29 Girls and 1 Boy in Group 2
If we continue in the same way, as the number of Boys in Group 1 goes down by 1, the number of Girls in Group 2 will also go down by 1, so the difference will always be 7.
Using a table
Image
Image
$$\begin{align}30-b&=37-a\\
-b+a&=37-30\\
a-b&=7\end{align}$$