SOLUTION: A certain two digit number Is two more than 3 times the units digit. If the digits if the number are interchanged, the resulting number is 24 less than 4 times the original number.

Question 551145: A certain two digit number Is two more than 3 times the units digit. If the digits if the number are interchanged, the resulting number is 24 less than 4 times the original number. Find the original number. Please help me solve this!!!!!!!
Found 3 solutions by JBarnum, josmiceli, MathTherapy:
Answer by JBarnum(2146)   (Show Source): You can put this solution on YOUR website!
wow im dizzy just reading this
two digit number will be: and ab= ex:10(1)+2=12
so
interchanged means which is
so
now we have 2 equations solve one equation for 1 variable then use substitution in other equation

.
simplify

substitute a
distribute 39
multiply all by 5
add like terms
add 81 and subtract 30b
divide

.

.
your number is
and interchanged is 92 lets check

correct

correct

that was fun got another one? Have a Happy New Year
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the 10's digit
Let = the 1's digit
given:
(1)
(2)
---------------------------
(1)
(1)
and
(2)
(2)
(2)
-------------------
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)

and, since
(1)
(1)
(1)
(1)
(1)
(1)
The original number is 29
check:
(2)
(2)
(2)
(2)
(2)
OK
Answer by MathTherapy(10558)   (Show Source): You can put this solution on YOUR website!

A certain two digit number Is two more than 3 times the units digit. If the digits if the number are interchanged, the resulting number is 24 less than 4 times the original number. Find the original number. Please help me solve this!!!!!!!

Let the tens and units digits be T & U, respectively

Because "A certain two digit number Is two more than 3 times the units digit."

Then:
10T + U = 3U + 2
10T � 2U = 2
5T � U = 1
U = 5T � 1 ---- eq (i)

Because, "the resulting number is 24 less than 4 times the original number," if the digits of the number are interchanged," then:

10U + T = 4(10T + U) � 24
10U + T = 40T + 4U � 24
- 39T + 6U = - 24 ---- eq (ii)

� 39T + 6(5T � 1) = - 24 ------ Substituting 5T � 1 for U in eq (ii)
- 39T + 30T � 6 = - 24
- 9T = - 18
T, or tens digit = , or , or

U = 5(2) � 1 ----- Substituting 2 for T in eq (i)
U = 10 � 1
U, or units digit =

Therefore, original number is

--------
Check
--------
29 = 3(9) + 2 ---- 29 = 27 + 2 ----- 29 = 29 (TRUE)
92 = 4(29) � 24 ----- 92 = 116 � 24 ---- 92 = 92 (TRUE)

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