Question

a said b "if you give me half your money i will have 400." b said a,"if you give me one thrid of your money, i will have 400" how much money did b have?

Answer 1

Answer : a + b*1/2 = 400

a*1/3 + b = 400

solving both equations,

a = 240

b = 320

Answer 2

Answer:

The money that b have 320

Step-by-step explanation:

Given that

a said if b gave half money  then it will have 400

[let x and y be the amount of the money that a and b have respectively]

⇒  $x + \frac{y}{2} = 400$  

⇒  $\frac{2x + y }{2} = 400$  

⇒  $2x + y = 800$ _(1)

b said if a gave one third of money then it will have 400

⇒  $y + \frac{x}{3} = 400$

⇒  $\frac{3y+ x }{3} =400$  

⇒  $3y + x =1200$

⇒  $x + 3y = 1200$ _ (2)

solve (1) and (2)  

 ⇒ 1 × (1)  =   $2x + y = 800$ _ (3)

 ⇒ 2× (2) =  $2 ( x + 3y = 1200)$ = $2x + 6y = 2400$_ (4)  

 ⇒ (4) - (3) ⇒  2x + 6y - (2x +y) = 2400 - 800

                 ⇒  2x + 6y -2x - y = 1600

                 ⇒  5y  = 1600

                 ⇒  y = 320

   (3) ⇒ 2x + 320 = 800  

                       2x = 480

                         x = 240    

the money that b have y = 320