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1. Lisa is 15 years old and her father is 40. How many years ago was the father six times as old as Lisa?

2. Joel is one third the age of Bob. In 7 years the combined ages of the boys will be 58. How old is each boy now?

3. Tom is three times as old as Leigh Ann. In 7 years, the sum of half of Tom's present age and a third of Leigh Ann's age will be the same as Tom's age now. How old will Tom be in 7 years?

  • math -

    Let it be x yrs ago, when Lisa was 15-x and her father was 40-x. Then-
    40-x=6(15-x) or 40-x=90-6x
    Or 6x-x=90-40 or 5x=50 thus x=5.

    Let Bob be x yrs and Joel be 3x. Then (x+7)+(3x+7)=58 or 4x+14=85
    Or 4x=44 hence x=11. Thus Bob is 11 and Joel is 33. After 7 yrs Bob willbe 18 and Joel will be 40. 18+40=58 OK.

    Let Leigh be x and Tom be 3x at present. After 7 yrs, Leigh will be x+7 and Tom will be 3x+7. Then,
    (x+7)/2 + (3x+7)/3=3x
    Or 2x+14+9x+21=3x
    Or, 7x=21+14=35 or x=5. Tom is 15.
    Check: After 7 yrs Leigh will be 12 and Tom will be 22.
    12/3 + 22/2=4+11=15. OK.

  • math -

    6(15-x) = 40-x
    Thus : x = 10

  • math -

    Question 1, X is supposed to be 10

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