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

Algebra ->  Equations -> 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       Log On


   

Question 1165899: 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=um of the digits. Find the number.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Instead of doing it for you, I'll do one exactly like yours step by step:

Five times the tens digit of a certain 2-digit number is 3 more than eight times the units digit.
The difference between the given number and the number obtained by reversing the digits is
six less than three times the sum of the digits. Find the number.
t = the tens digit
u = the units digit
10t+u = the number
10u+t = the number obtained by reversing the digits.

system%285t+=+8u+%2B+3%2C%0D%0A10t+%2B+u+-+%2810u+%2B+t%29+=+3%28t+%2B+u%29+-+6%29

Simplify the second equation

10t + u - (10u + t) = 3(t + u) - 6
  10t + u - 10u - t = 3t + 3u - 6
            9t - 9u = 3t + 3u - 6
           6t - 12u = -6

Divide through by 6

             t - 2u = -1

Solve for t

                  t = 2u - 1

Substitute in 

       5t = 8u + 3
5(2u - 1) = 8u + 3
  10u - 5 = 8u + 3
       2u = 8
        u = 4

Substitute in 

        t = 2u - 1
        t = 2(4) - 1
        t = 8 - 1
        t = 7

The number is 74.

Now use this as a model to solve yours by.

Edwin