The units’ digit of a two-digit number is 7 more than the tens’ digit. If 26 is added to the number, the result obtained is five times the sum of the digits. Find the number.

units diget cant be more than 9, so tens digit is 1 or 2.

18, or 29 is the number.
adding 26 to each
44, or 55 which is five times the sum of digits of the orginal number 18 or 29?

To find the two-digit number, let's represent it as "10x + y", where x is the tens digit and y is the units digit.

According to the given information, the units' digit (y) is 7 more than the tens' digit (x). So, we can write the equation:

y = x + 7 --- Equation 1

Furthermore, if 26 is added to the number (10x + y), the result is five times the sum of the digits (x + y). This can be represented as:

10x + y + 26 = 5(x + y) --- Equation 2

We can solve the system of equations (Equation 1 and Equation 2) to find the values of x and y, which will give us the two-digit number.

Substituting Equation 1 into Equation 2, we have:

10x + (x + 7) + 26 = 5(x + (x + 7))

Simplifying the equation:

10x + x + 7 + 26 = 5(2x + 7)

Combining like terms:

11x + 33 = 10x + 35

Subtracting 10x from both sides:

11x - 10x + 33 = 10x - 10x + 35

Simplifying:

x + 33 = 35

Subtracting 33 from both sides:

x + 33 - 33 = 35 - 33

Simplifying:

x = 2

Now that we have the value of x, we can substitute it back into Equation 1 to find y:

y = x + 7
y = 2 + 7
y = 9

So, the units digit (y) is 9 and the tens digit (x) is 2. Therefore, the two-digit number is 10x + y:

10(2) + 9 = 20 + 9 = 29

Hence, the two-digit number is 29.