Let x denote the number of pages holding 2 cards and y
denote the number of pages holding 3 cards.
So his entire number of card would be represented by 2x + 3y, which is given as
18.
2x + 3y = 18
Subtract 3y from the two sides:
2x = 18 – 3y
then divide both sides by 2:
x = (18 – 3y)/2
We know that x must be an integer. So 18 – 3y must be a multiple of 2. Since 18
is a multiple of 2, 3y is also a multiple of 2. Then y must be a multiple of 2
too.
Let's start with y = 0.
When y = 0, x = (18 – 3(0))/2 = 9.
When y = 2, x = (18 – 3(2))/2 = 6.
When y = 4, x = (18 – 3(4))/2 = 3.
When y = 6, x = (18 – 3(6))/2 = 0.
Thus there are 4 ways to display his figures.
