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Yesterday, 14:41

Tim is 4 years older than one-third of Juan's age. In 10 years, Juan will be 6 years older than twice as old as Tim is now. How old is each now?

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  1. Yesterday, 18:35
    0
    Juan's current age = 12

    Tim's current age = 8

    Step-by-step explanation:

    Let x = Juan's current age; x+10=Juan's age in 10 years

    Then (1/3) x+4=Tim's current age;

    Now we are told that:

    x+10=2{ (1/3) x+4}+6 eliminate brackets

    x+10 = (2/3) x+8+6 = (2/3) x+14 multiply both sides by 3

    3x+30=2x+42 subtract 30 and 2x from both side s

    3x-2x+30-30=2x-2x+42-30 collect like terms

    Juan's current age: x=12

    Tim's current age: (1/3) x+4 = (1/3) * 12+4=8

    4 years older than 1/3 of Juan's age = (1/3) * 12+4=8

    8=8

    In 10 years, Juan will be 6 years older than twice as old as Tim is now.

    12+10=22

    2*8+6=22

    22=22
  2. Yesterday, 18:35
    0
    Answer: Tim is 8 years old.

    Juan is 12 years old

    Step-by-step explanation:

    Let x represent the present age of Tim.

    Let y represent the present age of Juan.

    Tim is 4 years older than one-third of Juan's age. This is expressed as

    x = y/3 + 4

    In 10 years, Juan will be 6 years older than twice as old as Tim is now. This is expressed as

    2 (x + 10) = (y + 10) + 6

    2x + 20 = y + 16

    2x - y = 16 - 20

    2x - y = - 4

    2y/3 + 8 - y = 4

    2y + 24 - 3y = 12

    2y - 3y = 12 - 24

    - y = - 12

    y = 12

    Substituting y = 12 into x = y/3 + 4, it becomes

    12/3 + 4

    x = 4 + 4

    x = 8
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