SOLUTION: translate to a system of equations and solve. the sum of two numbers is 27. one half of the first number plus one third of the second number is 11. find the numbers

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Question 4993: translate to a system of equations and solve.
the sum of two numbers is 27. one half of the first number plus one third of the second number is 11. find the numbers
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
let the numbers be x and y
x+y=27.........[1]


one half of the first number plus one third of the second number is 11
1/2x+1/3y=11
(3x+2y)/6=11
3x+2y=66........[2]


x+y=27
multiply by 2
2x+2y=54.......[1]
3x+2y=66.......[2]


subtracting eqn 2 from 1 we get
2x+2y=54
3x+2y=66


-x=-12
x=12


y=27-x=27-12=15


Hence the numbers are:
12,15