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 figure? What is the problem sentence to this question.

Answer 1

Answer: The number of different ways can Roberto display his figure =4

Step-by-step explanation:

As per given , we have

Total cards = 18

Let 'a' be the number of pages with 2 cards and 'b' be the number of pages with 3 cards.

such that

$2a+3b=18$   (i)

Now , we need to find the possible solutions for (a,b) , where a, b are positive integers and satisfy equation (i).

When a=0 , $2(0)+3b=18\Rightarrow\ 3b=18\Rightarrow\ b=6$

When b=0 , $2a+3(0)=18\Rightarrow\2a=18\Rightarrow\ a=9$

When a=3 , $2(3)+3b=18\Rightarrow\ 6+3b=18\Rightarrow\ 3b=12\Rightarrow\ b=4$

When a=6 , $2(6)+3b=18\Rightarrow\12+3b=18\Rightarrow\ 3b=6\Rightarrow\ b=2$

i.e. Possible solutions for (a,b) = (0,6), (9,0) , (3,4) , (6,2) .

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

Thus , the number of different ways can Roberto display his figure =4

Answer 2

6 pages of 3; 4 pages of 3 and 3 pages of 2; 2 pages of 3 and 6 pages of 2; 9 pages of 2.  There are 4 ways to display his cards.  The problem sentence is 18=2x+3y