SOLUTION: Three times the tens digit of a certain 2 digit number is 2 more than four times the units digit. The difference between the given number and the number obtained by reversing the d

Question 1022958: Three times the tens digit of a certain 2 digit number is 2 more than four times the units digit. The difference between the given number and the number obtained by reversing the digits is two less than twice the sum of the digits. Find the number?

Found 2 solutions by addingup, stanbon:
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
let's call the number xy. Since x is the tens digit:
10x+y
The problem says:
3x = 4y+2 Subtract 4y from both sides:
3x-4y = 2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The difference between the given number and the number obtained by reversing the digits is two less than twice the sum of the digits:
10x+y-10y-x = 2(x+y)-2 Subtract on left and multiply on right:
9x-9y = 2x+2y-2 Subtract 2x and 2y on both sides:
7x-11y = -2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now we have two equations:
3x-4y = 2 (Multiply both sides of this equation times -7)
and
7x-11y = -2 (Multiply both sides of this equation times 3)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-21x+28y = -14
+
21x-33y = -6
---------------
. . -5y = -20
Divide both sides by -5
y = 4
Now that we know y let's find x. The problem says:
3x = 4y+2 substitute for y:
3x = 4(4)+2
3x = 16+2 Add on right and divide both sides by 3
x = 6
So, your tens digit is 6 and 6*10 = 60 and you singles digit is 4, and 60+4 = 64. This is your number: 64
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Three times the tens digit of a certain 2 digit number is 2 more than four times the units digit. The difference between the given number and the number obtained by reversing the digits is two less than twice the sum of the digits. Find the number?
====
Let the number be 10t + u
-----
Equations:
3t = 4u+2
10t+u-(10u+t) = 2(t+u)-2
---------------------------------
Rearrange::
3t - 4u = 2
9t - 9u = 2t+2u-2
-----
3t-4u = 2
7t - 11u = -2
-------------------
Modify for elimination::
21t - 28u = 14
21t - 33u = -6
------------------
Subtract and solve for "u"::
5u = 20
u = 4
----
Solve for "t"::
3t - 4u = 2
3t - 16 = 2
3t = 18
t = 6
----
Ans:: 10t+u = 64
---------------------
Cheers,
Stan H.
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