Question 240593
4 years ago Tom was twice as old as John. 4 years from now, John will be 3/4 Tom's age. How old are they now?
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Let Tom's age NOW be "t".
Let John's age NOW be "j".
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4 years ago Equation:
4 years ago Tom was twice as old as John.
(t-4) = 2(j-4)
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4 years from now Equation:
John will be (3/4) Tom's age.
(j+4) = (3/4)(t+4)
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So use those two equations to solve for "t" and for "j".
t-4 = 2j-8
j+4 = (3/4)t + 3
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t = 2j-4
j = (3/4)t - 1
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Substitute for "t" and solve for "j":
j = (3/4)(2j-4)-1
j = (3/2)j-3-1
(1/2)j = 4
j = 8 (John's age NOW)
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Substitute into t = 2j-4 to solve for "t":
t = 2*8-4 = 12 (Tom's age NOW)
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Cheers,
Stan H.