Question 256628
Kate is three years less than twice as old as her brother Brett. Next year Bretts age will be three fourths Kates age. How old is each now?
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Equations:
K = 2B-3
(B+1)= (3/4)(K+1)
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Rearrange:
4B+4 = 3K+3
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K = 2B-3
K = (4/3)B+1
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Solve 2B-3 = (4/3)B+1
(2/3)B = 4
B = 6 yrs (Brett's age NOW)
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Since K = 2B-3, K =2*6-3 = 9  (Katie's age NOW) 
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Cheers,
Stan H.