Question

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?

Answer 1

He could put 2 in each page 6 in two pages and 12 in 6 in another 2 in one page and 11 sets of three in the others and it just goes one

Answer 2

Answer:  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 ,

$3y=18\Rightarrow y=6$ , i.e. (0,6) is a solution .

At  y=0 ,

$2x=18\Rightarrow\ x=9$  , i.e. (9,0) is a solution.

At  x=3 ,

$2(3)+3y=18\Rightarrow\ 3y=12\Rightarrow\ y=4$  , i.e. (3,4) is a solution .

At  x=6 ,

$2(6)+3y=18\Rightarrow\ 3y=6\Rightarrow\ y=2$  , 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.