SOLUTION: Jane is four times as old as Jade.In six years,the quotient of Jane and Jade's ages willbe one less than Jade's present age.Find their present ages.
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Question 584730: Jane is four times as old as Jade.In six years,the quotient of Jane and Jade's ages willbe one less than Jade's present age.Find their present ages. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Let j = Jane's present age
Let d = Jade's present age
:
Write an equation for each statement:
:
"Jane is four times as old as Jade."
j = 4d
:
"In six years,the quotient of Jane and Jade's ages will be one less than Jade's present age."
() = d - 1
:
multiply both sides by (d+6)
j + 6 = (d+6)*(d-1)
:
FOIL the right side
j + 6 = d^2 - d + 6d - 6
;
subtract 6 from both sides
j + 6 = d^2 + 5d - 6 - 6
j = d^2 + 5d - 12
:
replace j with 4d
4d = d^2 + 5d - 12
;
Subtract 4d from both sides
0 = d^2 + 5d - 4d - 12
;
A quadratic equation
d^2 + d - 12 = 0
;
Factors to
(d+4)(d-3) = 0
;
the positive solution
d = 3 hrs old is Jade's present age
then obviously:
12 yrs is Jane's age
:
:
Check solution in the statement:
"In six years, the quotient of Jane and Jade's ages will be one less than Jade's present age."
() = 3 - 1 = 3 - 1
