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?
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
