Question

a , b, c, d and e are playing cards. In the game:
A says to B, If u give me three cards, u will have as many as E has and if I give u three cards, u will have as many as D has. A has three times the cards C has. If D has five cards more than what A has and the total no. of cards be 123.
1) How many cards does B have?
2) How many cards everyone has?
3) Explain the whole que, by writing the equ.

Answer 1

Answer :

Given : A , B, C, D and E are playing cards. In the game: A says to B, If u give me three cards, u will have as many as E has , So

E = B - 3 ---- ( 1 )

And , If I give u three cards, u will have as many as D has . SO

D = B + 3 ---- ( 2 )

And , If D has five cards more than what A has . So

D = A + 5 ---- ( 3 ) , Substitute value from equation 2 , we get

A + 5 = B + 3

A = B - 2 ---- ( 4 )

And
A has three times the cards C has
So,
A = 3C ---- ( A ) , Substitute value from equation 4 , we get

3C = B - 2 , So

C = $\frac{B-2}{3}$ ---- ( 5 )
Add equation 1 and 2 , we get

D + E = 2 B ------ ( 6 )

And

The total no. of cards be 123 , So

A + B + C + D + E = 123 , Substitute values from equation 4 , 5 and 6 and get

$\Rightarrow$B - 2 + B + $\frac{B-2}{3}$ + 2B = 123

$\Rightarrow$4B - 2 + $\frac{B-2}{3}$ = 123

$$\begin{gathered} \Rightarrow \frac{12B-6+B-2}{3}=123 \\ \Rightarrow \frac{13B-8}{3}=123 \\ \Rightarrow 13B-8=369 \\ \Rightarrow 13B=377 \\ \Rightarrow B=\frac{377}{13} \\ \Rightarrow \mathit{B}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathbf{29} \end{gathered}$$

1 ) B have total cards = 29 ( Ans )

2 ) From equation 4 , we get

A = 29 - 2 = 27 , So A have 27 cards

From equation A , we get

3C = 27

So,

C = 9 , So C have 9 cards

From equation 1

E = 29 - 3 = 26 , So E have 26 cards

From equation 2

D = 29 +3 = 32 , So D have 32 cards

Then

Cards everyone has :

A = 27 , B = 29 , C = 9 , D = 32 and E = 26 ( Ans )


C ) Answered itself