Mathematics: 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.

12 would be the length of the blue line...

Roberto wants to display his 18 cards in an album.

myelee123

13.03.2022

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

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