the units of a number is 4 more than the tens digit. If the digits are reversed the new number is 1 less than twice the original number. Use a system of equations and substitution to find the number.
I'm stuck?!?!
To solve this problem using a system of equations, let's start by assigning variables to the unknowns. Let the tens digit be represented by 'T' and the units digit by 'U'.
From the problem statement, we can form the following two equations:
1) The units digit is 4 more than the tens digit: U = T + 4
2) When the digits are reversed, the new number is 1 less than twice the original number: 10U + T = 2(10T + U) - 1
Now, we can substitute the value of U from equation 1 into equation 2:
10(T + 4) + T = 2(10T + (T + 4)) - 1
10T + 40 + T = 2(11T + 4) - 1
11T + 40 = 22T + 8 - 1
11T + 40 = 22T + 7
Next, let's simplify the equation:
11T - 22T = 7 - 40
-11T = -33
Divide both sides of the equation by -11 to solve for T:
T = (-33)/(-11)
T = 3
Now, substitute the value of T back into equation 1 to find the value of U:
U = T + 4
U = 3 + 4
U = 7
So, the tens digit is 3 and the units digit is 7. Therefore, the number is 37.
Let x be the units digit and y be the tens digit.
"The units of a number is 4 more than the tens digit"
x = y + 4
"If the digits are reversed the new number..."
The original number is x + 10y. The reversed number is 10x + y.
"...is 1 less than twice the original number."
10x + y = 1 + 2(x + 10y)