SOLUTION: The sum of two numbers is 54 and their difference is nine more than the smaller number. Find the numbers.

Question 279600: The sum of two numbers is 54 and their difference is nine more than the smaller number. Find the numbers.
Found 2 solutions by mananth, richwmiller:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let the number be x
the other number will be 54-x
x-(54-x)=x+9
2x-54=x-9
x=45
the other number = 12

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
sorry but 45+12 =57 NOT 54
y+x=54
y-x=x+9
2y=x+63
2y-63=x
x=2y-63
x=54-y
2y-63=54-y
3y=117
y=39
y+x=54
39+x=54
x=15
x=15 y=39
check
39+15=54
39-15=15+9
24=24
ok
x=15 y=39
also adapting the other tutor's method
54-x-x=x+9
54-2x=x+9
45=3x
15=x
54-15=39
the numbers are 15 and 39
or even
x-(54-x)=54-x+9
x-54+x=63-x
2x-54=63-x
3x=117
x=39
54-x=15
again the numbers are 15 and 39
What did the other tutor do wrong?
he used the larger number plus 9 not the smaller number plus 9
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