Multiply the digits of a two digit number by 6 Find the number if 9 is subtracted from that number and the digits of the original number are reversed.
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A number of two digits is six times the sum of its digit. If 9 is subtracted from the number, the digits are reversed. What is the number?
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7 Answers

Kurt Mager, Enjoys solving math problems
Answered September 26, 2019
The number is 54.
A number of two digits
10x+y
is six times the sum of its digit.
10x+y=6(x+y)
10x+y=6x+6y
If 9 is subtracted from the number, the digits are reversed.
10x+y-9=10y+x
What is the number?
10x-x+y-9=10y+x-x
9x+y-y-9=10y-y
(9x-9)/9=9y/9
y=x-1
10x+y=6x+6y
10x+x-1=6x+6(x-1)
11x-6x-1=6x-6x+6x-6
5x-5x-1=6x-5x-6
-1+6=x-6+6
x=5
10(5)+y=6(5)+6(y)
50–30+y=30-30+6y
20+y-y=6y-y
20/5=5y/5
y=4
Verify:
10x+y=6x+6y
6x=30
6y=24
50+4=30+24
10x+y-9=10y+x
50+4–9=40+5
54–9=45
So the number is 54.
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