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

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) (Show Source): You can put this solution on YOUR website!
Let t=tens digit and u=units digit

So the unknown number is

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

Start with the second equation.

Plug in

Plug in

Multiply.

Combine like terms on the left side.

Subtract from both sides.

Combine like terms on the left side.

Divide both sides by to isolate .

Reduce.

So the tens digit is .

Go back to the first equation

Plug in

Multiply

So the units digit is . This means that the number is

Answer by mangopeeler07(462) (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

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.
RELATED QUESTIONS
I have a word problem that I need some help with. The sum of the digits of a... (answered by nerdybill)
Please help me solve this word problem: The sum of the digits of a two-digit number is... (answered by Theo)
Please help me solve this word problem: My tens digit is 4 less than thousand digit is... (answered by Edwin McCravy)
This word problem is stumping me. I can't figure out how to write the equations needed... (answered by longjonsilver)
This is a digit and coin word problem. I know how to do simpler digit and coin problems... (answered by Edwin McCravy)
Please help me solve this word problem leading to quadractic The sum of the digits of a... (answered by ankor@dixie-net.com)
Please help me solve this equation: {{{ the unit digit of a number is more than twice the (answered by Theo)
Please help me to solve this problem. What is the three digit odd number where the sum... (answered by Edwin McCravy)
please help me with this problem..thank you! the sum of the digits of a three digit... (answered by scott8148)