This morning, Jim had half as much money as his brother and $27 dollars less than his sister. Then his brother paid Jim and his sister each $12 dollars to take the dogs out for a walk. After the payoff, Jim's brother had half as much money as Jim's sister. How much money does Jim have now?

Answer:Jim has $37.67Step-by-step explanation:Let in the morning Jim had $x, his brother had $y and his sister had $z.Jim had half as much money as his brother.So, [tex]x = \frac{y}{2}[/tex] ........ (1)And Jim had $27 less than his sister.So, x = z - 27 ........ (2)⇒ [tex]\frac{y}{2} = z - 27[/tex] {From equation (1)}⇒ y = 2z - 54⇒ 2z - y =54 ..........(3)Now, his brother paid Jim and his sister each $12.Therefore, now, Jim has $(x + 12), his brother has $(y -24) and his sister has $(z + 12).Given that after payoff, Jim's brother has half as much money as Jim's sister.So, [tex]\frac{z + 12}{2} = y - 24[/tex]⇒ z + 12 = 2y - 48⇒ 2y - z = 50 ......... (4)Now, solving equations (3) and (4), we get3y = 54 + 100 = 154⇒ y =  51.33.Now, from equation (3),we have z = 52.67And from equation (1), [tex]x=\frac{51.33}{2} =25.67[/tex]So, now, Jim has (25.67 + 12) = $37.67 (Answer)