SOLUTION: please help me determine the equation and solution to this word problem. Twice the tens digit of a number is the same as the units digit. The number is 6 greater than 5 times t

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Question 150546: please help me determine the equation and solution to this word problem.
Twice the tens digit of a number is the same as the units digit.
The number is 6 greater than 5 times the units digit.
Find the number.
Found 2 solutions by jim_thompson5910, mangopeeler07:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let t=tens digit and u=units digit

So the unknown number is n=10t%2Bu


Since "Twice the tens digit of a number is the same as the units digit", this means that 2t=u (or u=2t). Also, because the "number is 6 greater than 5 times the units digit", this means that n=5u%2B6


n=5u%2B6 Start with the second equation.


10t%2Bu=5u%2B6 Plug in n=10t%2Bu


10t%2B2t=5%282t%29%2B6 Plug in u=2t


10t%2B2t=10t%2B6 Multiply.


12t=10t%2B6 Combine like terms on the left side.


12t-10t=6 Subtract 10t from both sides.


2t=6 Combine like terms on the left side.


t=%286%29%2F%282%29 Divide both sides by 2 to isolate t.


t=3 Reduce.


So the tens digit is t=3.


u=2t Go back to the first equation


u=2%283%29 Plug in t=3


u=6 Multiply


So the units digit is u=6. This means that the number is n=36


Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
t=tens digit
u=units digit
x=number we're looking for

2t=u
x=5u+6

0%3Cu%3C10
Plug in a value from this range
try 1

2t=1
t=1/2
not a digit

try 2
2t=2
t=1
that would make the number 12.
x=5u+6
x=5(2)+6
x=16, not 12

try 3
2t=3
t=3/2
not a digit
*following this pattern, we see that the units is an even number, since odds give us non-digits.

try 4
2t=4
t=2
that would make the number 24
x=5(4)+6
x=26, not 24

try 6
2t=6
t=3
That would make the number 36
x=5(6)+6
x=36
It works.

Therefore, the number is 36.