SOLUTION: Kate is three years less than twice as old as her brother Brett. Next year Bretts age will be three forths Kates age. How old are each?

Question 256726: Kate is three years less than twice as old as her brother Brett. Next year Bretts age will be three forths Kates age. How old are each?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let k = Kate's age now
let b = Brett's age now
:
Write an equation for each statement:
;
"Kate is three years less than twice as old as her brother Brett."
k = 2b - 3
:
"Next year Bretts age will be three fourths Kate's age."
b + 1 = (k + 1)
Multiply by 4, results;
4b + 4 = 3(k + 1)
4b + 4 = 3k + 3
4b = 3k + 3 - 4
4b = 3k - 1
Using the 1st equation, replace k with (2b-3)
4b = 3(2b-3) - 1
4b = 6b - 9 - 1
4b = 6b - 10
+10 = 6b - 4b
10 = 2b
b = 5 yrs is Brett's present age
then
k = 2(5) - 3
k = 7 yrs is Kate's present age
;
:
Check solutions in the statement:
"Next year Bretts age will be three fourths Kate's age."
5 + 1 = (7 + 1)
6 = *8
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