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) (Show Source): You can put this solution on YOUR website!
A and B present or current ages.
Solve the system for A and B:
Answer by mark_henrhiz(40) (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.
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