SOLUTION: ten years from now,A will be twice as old B and five years ago,A was three times as old as B. what are the present age of A and B.

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Question 894306: ten years from now,A will be twice as old B and five years ago,A was three times as old as B. what are the present age of A and B.
Found 2 solutions by josgarithmetic, mark_henrhiz:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A and B present or current ages.

A%2B10=2%28B%2B10%29
A%2B10=2B%2B20
A-2B=10

A-5=3%28B-5%29
A-5=3B-15
A-3B=-10

Solve the system for A and B:
highlight%28system%28A-2B=10%2CA-3B=-10%29%29

Answer by mark_henrhiz(40) About Me  (Show Source):
You can put this solution on YOUR website!
their ages 10 years from now are:

A+10
B+10

Their ages 5 years ago are:

A-5
B-5

Translating to equations:
A+10 = 2(B+10)
A+10 = 2B+20
A-2B = 20-10
A-2B = 10 FIRST EQUATION

A-5 = 3(B-5)
A-5 = 3B-15
A-3B = -15+5
A-3B = -10 SECOND EQUATION
THUS,

A-2B = 10
A-3B = -10


WE CAN SOLVE THIS EITHER BY ADDITION METHOD OR SUBSTITUTION METHOD.

THROUGH ADDITION METHOD

(A-2B = 10)-1 WE MULTIPLY -1 TO THE FIRST EQUATION TO GET RID OF "A"
+(A-3B =-10) IN ORDER TO FIND THE VALUE OF "B"
HENCE,
-A+2B = -10
+A-3B = -10 WE ADD
-B = -20 WE DIVIDE BOTH SIDES WITH -1
B = 20
WE CAN NOW SOLVE FOR "A" USING EITHER OF THE TWO EQUATIONS
A - 2B = 10
A-2*20 = 10 SUBSTITUTE 20
A-40 = 10
A = 10 + 40
A = 50
THEREFORE, "A" IS 50 YEARS OLD WHILE "B" IS 20 YEARS OLD NOW.