Question

A 2-digit number is 12 times its tens digit. The sum of the digits is 12. Determine the tens digit by setting up a system of equations.

a) 1
b) 2
c) 3
d) 4

Equations:
Let the tens digit be T and the units digit be U.
1. ( 10T + U = 12T )
2. ( T + U = 12 )

Answer 1

To determine the tens digit of a 2-digit number that is 12 times its tens digit and has a sum of digits equal to 12, we can set up a system of equations and solve it.

Step-by-step explanation:

To determine the tens digit of a 2-digit number that is 12 times its tens digit and has a sum of digits equal to 12, we can set up a system of equations:

1. 10T + U = 12T, where T represents the tens digit and U represents the units digit.
2. T + U = 12

To solve this system, we can substitute the second equation into the first equation:

1. 10T + (12 - T) = 12T
2. 10T + 12 - T = 12T
3. 12 + 12 = 12T - 10T + T
4. 24 = 3T
5. T = 8

Therefore, the tens digit is 8.