SOLUTION: The units digit of a number is 4 more than the tens digit. If the digits are reversed, the new number is 1 less than twice the origional number. Use a system of equations and sub

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The units digit of a number is 4 more than the tens digit. If the digits are reversed, the new number is 1 less than twice the origional number. Use a system of equations and sub      Log On


   

Question 139578: The units digit of a number is 4 more than the tens digit. If the digits are reversed, the new number is 1 less than twice the origional number. Use a system of equations and substitution to find the number.
I need to know how to set up the system of equations for this problem and what steps to take to solve it. Thank you.
Found 2 solutions by oscargut, solver91311:
Answer by oscargut(2103) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number ab
The units digit of a number is 4 more than the tens digit
then b=a+4
If the digits are reversed, the new number is 1 less than twice the origional number.
The number with the digits reversed is ba
then 10b+a=2(10a+b)-1
substitute in the last equation
then
10(a+4)+a=2(10a+(a+4))-1
11a+40=20a+2(a+4)-1
11a+40=22a+7
-11a=-33
a=3
b=7
Answer: the number is 37



Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the tens digit and y be the units digit.

The first bit of data tells you that y=x%2B4 (Equation 1)

The value of the original number is 10x%2By, just like 47=10%284%29%2B7

The new number with the digits reversed would then be 10y%2Bx

Twice the original number would be 2%2810x%2By%29 and 1 less than that would be 2%2810x%2By%29-1, so:

10y%2Bx=2%2810x%2By%29-1 (Equation 2)

Because Equation 1 is already solved for y, the easiest solution method is by substitution. In Equation 2, distribute the 2 across 10x%2By, get the variables on the left and leave the constant on the right, collect like terms, and then substitute the value of y, namely x+%2B+4 for the y in the re-arranged version of Equation 2. Then solve for x. Once you have x, you can easily obtain y by substitution in Equation 1.