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

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) (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) (Show Source): You can put this solution on YOUR website!
Let be the tens digit and be the units digit.

The first bit of data tells you that (Equation 1)

The value of the original number is , just like

The new number with the digits reversed would then be

Twice the original number would be and 1 less than that would be , so:

(Equation 2)

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

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