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

Question

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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Katherine 2 weeks 2021-09-09T16:24:13+00:00 2 Answers 0

Answers ( )

    0
    2021-09-09T16:25:29+00:00

    Answer:

    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

    0
    2021-09-09T16:25:30+00:00

    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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