Question 20668
Answer 9943 by venugopalramana(368) About Me  on 2005-11-27 11:27:42 (Show Source):
SEE MY COMMENTS IN CAPITAL LETTERS
Can anyone help with this problem?
The tens digit of a two-digit number is 7 less than twice the units digit. If the digits are reversed, the new number is 13 more than twice the original number. Find the original number.
I started with
x = units............OK
y = tens .....SO THE NUMBER IS YX.....AND ...[2x-7=y]......GOOD..NOW YOU BETTER WRITE THE VALUE OF THIS NUMBER
VALUE OF NUMBER = 10Y+X=10(2X-7)+X=20X-70+X=21X-70
NOW THE DIGITS ARE REVERSED...SO THE NUMBER IS XY...THE VALUE OF THIS NUMBER IS
10X+Y =10X+2X-7=12X-7...NOW WE ARE GIVEN THAT
2*(21X-70)+13=12X-7.
42X-140+13=12X-7
42X-12X=140-13-7=120
30X=120
X=4
SO Y = 2X-7=2*4-7=1
SO THE ORIGINAL NUMBER IS YX = 14....WHICH YOU CAN EASILY VERIFY..NOW YOU DID EXTREMELY WELL I SHOULD SAY BUT MADE A SMALL AITHMATIC ERROR AS SHOWN BELOW
2(10y + x )+ 13 = 10x + y..............EXCELLENT
but end up with
y = 8/19x - 13/19...VERY GOOD
2x-7 = 8/19x + 13/9..............HOW YOU MADE A SIMPLE COPYING MISTAKE..IT IS
2X-7=(8/19)X-13/19..SO
(30/19)X=120/19
X=(120/19)*(19/30)=4..GOT IT ....I AM REALLY IMPRESSED BY YOUR WORKING IT IS VERY GOOD AND YOU GOT THE ANSWER ALMOST EXCEPT FOR THAT SIMPLE MITAKE...CONCENTRATE A BIT MORE AND YOU WILL SUCCEED..GOD LUCK
but ended up with
30/19x = 76/9.....
I know the answer is 14
but I am so lost!l Please help!
Thanks,
Sandy
0 solutions