Question 894306
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        
<b>A-2B = 10</b>    FIRST EQUATION

        
A-5  = 3(B-5)
A-5  = 3B-15
A-3B = -15+5
<b>A-3B  = -10</b>    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"
+<u>(A-3B =-10)</u>       IN ORDER TO FIND THE VALUE OF "B"

HENCE,

-A+2B = -10
+<u>A-3B = -10</u>    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.