Roberto wants to display his 18 cards in an album. some pages hold 2 cards and others hold 3 cards. how many different ways can roberto display his figures?

 4

Step-by-step explanation:

Given , Roberto wants to display his 18 cards in an album.   (i)

Let x= Number of pages that hold 2 cards

y=  Number of pages that hold cards.

Then , total cards = 2x+3y

From  (i) , we have 2x+3y=18    ... (ii)

Now , Number of different ways Roberto displays his figures =Number of possible solutions for (x,y) , where x and y are any positive integers .

At x=0 ,

, i.e. (0,6) is a solution .

At  y=0 ,

 , i.e. (9,0) is a solution.

At  x=3 ,

 , i.e. (3,4) is a solution .

At  x=6 ,

 , i.e.  (6,2) is a solution .

Since , Number of possible solutions for (a,b) =4

Therefore, the required number of different ways can Roberto display his figure is 4.

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step-by-step explanation: