Roberto wants to display his 18 sports cards in an album. Some pages hold 2 cards and others hold 3 cards. How many different ways can Roberto display his figures?

Let x = number of pages holding 2 cards,

y = number of pages holding 3 cards.

So his total number of card would be 2x + 3y, which is given as 18. So we get this equation.

2x + 3y = 18

Subtract 3y from both sides:

2x = 18 - 3y

Divide both sides by 2:

x = (18 - 3y) / 2

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.