Question

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 1

$29

Explanation:

By running through the question we find,

i. Jim = Brother/2

ii. Jim = Sister - 27

iii. Jim = Jim + 12

iv. Sister = Sister + 12

v. Brother - 24 = Sister + 12/2

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By looking at above equations we know that,

Jim = Sister - 27

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where from equation iii and iv, Jim = Jim + 12 and Sister = Sister + 12

Jim + 12 = Sister + 12 - 27

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where, from equation v, Brother - 24 = Sister + 12/2 => Sister + 12 = 2(Brother - 24)

Jim + 12 = 2(Brother -24) - 27

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where from equation i, Jim = Brother/2 => Brother = 2*Jim

Jim + 12 = 2(2*Jim - 24) - 27

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Hence,

Jim + 12 = 4*Jim - 48 - 27

Jim + 12 = 4*Jim - 75

Jim - 4*Jim + 12 = -75

Jim - 4*Jim = -75 - 12

Jim(1 - 4) = -87

Jim(-3) = -87

Jim = -87/-3

Jim = 29

Answer 2

Jim has $37.67

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,
`x = (y)/(2)` ........ (1)

And Jim had $27 less than his sister.

So, x = z - 27 ........ (2)

⇒
`(y)/(2) = z - 27` {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,
`(z + 12)/(2) = y - 24`

⇒ z + 12 = 2y - 48

⇒ 2y - z = 50 ......... (4)

Now, solving equations (3) and (4), we get

3y = 54 + 100 = 154

⇒ y = 51.33.

Now, from equation (3),we have z = 52.67

And from equation (1),
`x=(51.33)/(2) =25.67`

So, now, Jim has (25.67 + 12) = $37.67 (Answer)