Question 19786
let the larger number be x
let the smaller number be y
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difference of two numbers means (x-y)
this difference is nine more than the smaller number
x-y=9+y
x-y-y=9
x-2y=9......[1]
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the sum of the two numbers is 54
x+y=54.......[2]
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take the two equations together,
x-2y=9
x+y=54
subtract equation [2] from [1]
x-2y-(x+y)=9-54
x-2y-x-y=-45
-3y=-45
3y=45
y=15
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x+y=54
x=54-y=54-15=39
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x=39,y=15
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Hope this helps,
Prabhat