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.

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^