The sum of the digits of a positive two-digit number is 13,If twice the first digit is 1 less than the second digit,what is the two-digit number ?
49, 58, 67, 76, 85, or 94
Let t = ten's digit
Let x = one's digit
t + x = 13
2t= x-1 or 2t+1 = x
You can substitue for "x"
t + 2t + 1 = 13
3t = 12
t = 4 find x = 9
so we have 49
To find the two-digit number, we need to use the given information to solve the problem step by step.
Let's start by writing down what we know:
1) The sum of the digits of the two-digit number is 13.
2) Twice the first digit is 1 less than the second digit.
Now, let's assign variables to the unknowns in the problem. We can use "x" for the first digit and "y" for the second digit. Therefore, the two-digit number can be represented as 10x + y.
According to the information given, we can write two equations:
1) x + y = 13 (since the sum of the digits is 13)
2) 2x = y - 1 (since twice the first digit is 1 less than the second digit)
To solve this system of equations, we can use substitution or elimination methods. Let's use substitution in this case.
From equation 2, we can rewrite it as y = 2x + 1.
Now substitute this expression for y in equation 1:
x + (2x + 1) = 13
3x + 1 = 13
3x = 13 - 1
3x = 12
x = 12/3
x = 4
Now substitute the value of x back into equation 2 to find y:
y = 2(4) + 1
y = 8 + 1
y = 9
So, the first digit is 4 and the second digit is 9. Therefore, the two-digit number is 49.