The sum of the digits of a two-digit number is 13. The units digit is one more than twice the tens digit. What is the number?

49

Let's use algebra to solve this problem step-by-step.

Let's assume the tens digit is represented by the variable 'x', and the units digit is represented by the variable 'y'.

According to the given information, we can form two equations:

1. The sum of the digits is 13: x + y = 13

2. The units digit is one more than twice the tens digit: y = 2x + 1

Now we have a system of linear equations. We can solve them simultaneously to find the values of x and y.

Let's start by solving equation 2 for x:

y = 2x + 1

Subtract 1 from both sides of the equation:

y - 1 = 2x

Now divide both sides of the equation by 2:

(x + y - 1)/2 = x

Now substitute this value of x into equation 1:

x + y = 13

(x + (2x + 1) - 1)/2 + (2x + 1) = 13

(3x + 1)/2 + (2x + 1) = 13

Multiply everything by 2 to get rid of the fractions:

3x + 1 + 4x + 2 = 26

7x + 3 = 26

Subtract 3 from both sides of the equation:

7x = 23

Divide both sides of the equation by 7:

x = 23/7

The value of x is a fraction, which is not possible since we are looking for a two-digit number.

Therefore, there is no two-digit number that satisfies the given conditions.

To find the number, we can set up some equations based on the given information.

Let's represent the tens digit as "x" and the units digit as "y".

According to the problem, the sum of the digits is 13. So we can write the equation:

x + y = 13 ---(equation 1)

It is also given that the units digit is one more than twice the tens digit. Mathematically, we can express this as:

y = 2x + 1 ---(equation 2)

Now we have a system of equations. We can use this system to solve for the values of x and y, which will give us the two-digit number.

Substitute equation 2 into equation 1:

x + (2x + 1) = 13

Combine like terms:

3x + 1 = 13

Subtract 1 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Now substitute the value of x back into equation 2:

y = 2(4) + 1

Simplify:

y = 9

The tens digit (x) is 4 and the units digit (y) is 9, so the number is 49.

4 and 9

5 and 8
6 and 7

Which of those pairs meet the other criterion?