SOLUTION: Kate is three years less than twice as old as her brother Brett. Next year, Brett's age will be three fourths Kate's age. How old is each now?

Question 589050: Kate is three years less than twice as old as her brother Brett. Next year, Brett's age will be three fourths Kate's age. How old is each now?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let k = K's present age
let b = B's present age
;
Write an equation for each statement:
:
"Kate is three years less than twice as old as her brother Brett."
k = 2b-3
:
" Next year, Brett's age will be three fourths Kate's age."
b + 1 = .75(k+1)
b + 1 = .75k + .75
b = .75k + .75 - 1
b = .75k -.25
Replace k with (2b-3)
b = .75(2b-3) - .25
b = 1.5b - 2.25 - .25
b = 1.5b - 2.5
2.5 = 1.5b - b
2.5 = .5b
multiply both sides by 2
b = 5 yrs is B's age
then
k = 2(5) - 3
k = 7 yrs is K's age
:
:
:
Check solutions in the statement:
" Next year, Brett's age will be three fourths Kate's age."
5 + 1 = .75(7+1)
6 = .75(8)

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