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

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?

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Kylie 2 weeks 2021-11-21T11:40:01+00:00 2 Answers 0

Answers ( )

    0
    2021-11-21T11:41:01+00:00

    Answer:

    Jim has $37.67

    Step-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, x = \frac{y}{2} …….. (1)

    And Jim had $27 less than his sister.

    So, x = z – 27 …….. (2)

    \frac{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, \frac{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=\frac{51.33}{2} =25.67

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

    0
    2021-11-21T11:41:06+00:00

    Answer:

    $29

    Step-by-step 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

    /////////////////////////////////////////////////////////////////////////////

    By looking at above equations we know that,

    Jim = Sister – 27

    /////////////////////////////////////////////////////////////

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

    Jim + 12 = Sister + 12 – 27

    /////////////////////////////////////////////////////////////

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

    Jim + 12 = 2(Brother -24) – 27

    /////////////////////////////////////////////////////////////

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

    Jim + 12 = 2(2*Jim – 24) – 27

    /////////////////////////////////////////////////////////////////////////////

    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

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