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Question

four times the 10's digit of a 2 digit number increased by the unit digit is 18. if the digits are reversed, the new number is 9 less than twice the original number. find the original number.
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Answer 1

T = ten's digit of original number
and the unit's digit when the digits are reversed

U = unit's digit of original number
and the ten's digit when the digits are reversed

10T + U = value of original number
10U + T = value of reversed digit number

4T + U = 18
10U + T = 2(10T + U) - 9

4T + U = 18
10U + T = 20T + 2U - 9

4T + U = 18
-19T + 8U = -9

Solve the first equation for U and substitute
U = 18 - 4T

-19T + 8(18 - 4T) = -9

-19T + 144 - 32T = -9

-51T = -153

T = 3

U = 18 - 4T = 18 - 4(3) = 18 - 12 = 6

The original number is 36

Answer 2

Take all the single digit numbers and multiply them by 4, you'll quickly see that everything 5 and up is automatically out because they are already bigger then 18 before I add anything to them.

Zero is out because if I multiply by 4 the result is zero and there is no single digit large enough to add to zero to make 18. The same is true for 1 and 2 so the only numbers that could be in the tens digit is 3 or 4.

Using the theory that

3 x 4 = 12 and that we're adding to 18, the other digit would have to be 6

or 4 x 4 = 16 and that we're adding to 18, the other digit would have to be 2

so the numbers on the table are 36 or 42.

Now flip the numbers around so we have 63 and 24. Add nine to both and we have 72 and 32, which is double the original? 72 is which reversed as 63 which started as 36.

Answer 3

10X + Y = ?

4X + Y = 18
10Y + X = 20X + 2Y - 9

8Y = 19X - 9
Y = 18 - 4X
-8Y = -144 + 32X
0 = -153 + 51X
X = 3

4X + Y = 18 = 12 + Y
Y = 6

original number = 36

Answer 4

4T + U = 18
U = 18 - 4T

2(10T + U) - 9 = 10U + T
20T + 2(18 - 4T) - 9 = 10(18 - 4T) + T
20T + 36 - 8T -9 = 180 - 40T + T
51T = 153
T = 3

U = 18 - 4(3)
U = 6

The number is 36

Answer 5

0, the answer is 0.

Answer 6

4x ................ cudn b arsed soz