SOLUTION: The sum of the digits of a two-digit number is 7. If the digits are reversed, the new number increased by 3 equals 4 times the original number. Find the original number.

Question 113520This question is from textbook Arithmetic and algebra again
: The sum of the digits of a two-digit number is 7. If the digits are reversed, the new number increased by 3 equals 4 times the original number. Find the original number.

here is what I have done:

original number 10x + y
new number 10y + x
x + y = 7

10x + y = 10y + x + 3
10x -x + y -y = 10y -y + x -x + 3
9x = 9y + 3
x = y + 3

x + y = 7
(y+3) + y = 7
2y + 3 = 7
2y +3 -3 = 7 -3
2y = 4
2y/2 = 4/2
y = 2
x + y = 7
2 + y = 7
2 -2 + y = 7 -2
y = 5
x = 2
I get an answer, but it don't check.
Every time I do this problem this my answer or fractional. please help This question is from textbook Arithmetic and algebra again

Found 3 solutions by kev82, Fombitz, MathLover1:
Answer by kev82(151)   (Show Source): You can put this solution on YOUR website!
It's great to see someone posting their working and, not only that but checking the answer as well, realising they've done something wrong. These are great traits that you should be proud of. Anyway, to the problem, you have only made a very slight mistake:
"If the digits are reversed, the new number increased by 3 equals 4 times the original number"
so 10y+x+3 = 4(10x+y). This tidies up to 6y-39x = -3. Combining this with y=7-x gives 6(7-x)-39x=-3, 42-45x=-3, 45x=45 x=1, y=6.

Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Your analysis is correct and you're on the right track.
You made a mistake at this point.

The new number (digits reversed) increased by 3 equals 4 times the original number.
You forgot the 4.

Now together with

should get you a quick answer.
Good luck.
Post another question if you get stuck.

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
here is one more solution to this problem...

Let ten's digit be and unit's digit be . Then,
of the digits =
The number is =

of the digits is ,
��..�(1)
When the digits are reversed, the new number becomes
=
New number increased by 3 = 4 times the original number
(10y + x) + 3 = 4 (10x + y)
or 10y + x + 3 = 40x + 4y

�� (Dividing by 3) �(2)
(1) by 2, we get,
��..�(3)
(3) from (2),
��..��..(2)
��..�(3)
��.=>��
Substituting in (1) we will have
��=>�
So, the number is

When the digits are reversed, the new number is
Check:

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