A NUMBER CONSISTS OF TWO DIGITS IN WHICH THE TENS DIGIT EXCEEDS THE UNITS DIGIT BY 6. THE NUMBER ITSELF IS EQUAL TO TEN TIMES THE SUM OF DIGITES. FIND THE NUMBER

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Solution

LET Y (UNITS DIGIT) PLUS 6 EQUAL THE TENS DIGIT X
Y=X-6
10(X+Y)=10X+Y REPLACE Y WITH (X-6)
10(X+X-6)=10X+(X-6)
10(2X-6)=10X+X-6
20X-60=11X-6
20X-11X=60-6
9X=54

X=54/9
X=6 WHICH IS THE TENS DIGIT
Y=6-6=0 FOR THE UNITS DIGIT'
PROOF
10(6+0)=10*6+0
60=60

The number is 60

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A NUMBER CONSISTS OF TWO DIGITS IN WHICH THE TENS DIGIT EXCEEDS THE UNITS DIGIT BY 6. THE NUMBER ITSELF IS EQUAL TO TEN TIMES THE SUM OF DIGITES. FIND THE NUMBER

LET Y (UNITS DIGIT) PLUS 6 EQUAL THE TENS DIGIT X Y=X-6 10(X+Y)=10X+Y REPLACE Y WITH (X-6) 10(X+X-6)=10X+(X-6) 10(2X-6)=10X+X-6 20X-60=11X-6 20X-11X=60-6 9X=54 X=54/9 X=6 WHICH IS THE TENS DIGIT Y=6-6=0 FOR THE UNITS DIGIT' PROOF 10(6+0)=10*6+0 60=60 The number is 60

LET Y (UNITS DIGIT) PLUS 6 EQUAL THE TENS DIGIT X
Y=X-6
10(X+Y)=10X+Y REPLACE Y WITH (X-6)
10(X+X-6)=10X+(X-6)
10(2X-6)=10X+X-6
20X-60=11X-6
20X-11X=60-6
9X=54

X=54/9
X=6 WHICH IS THE TENS DIGIT
Y=6-6=0 FOR THE UNITS DIGIT'
PROOF
10(6+0)=10*6+0
60=60

The number is 60