Question

Follow the process for establishing a set of equations:

1. Choose a varlable to represent one of the unknowns.
2. Express the remaining unknowns in terms of the varlable you chose in step 1. Look for a relationship between the
unknowns glven in the problem.
3. Write an equation. (Look for the other relationship given in the problem.)
The tens digit of a number is twice the ones digit. The sum of the digits in the number is 12. What is the number?
Include the entire process for establishing a set of equations, the solution, and an explanation of what the solution
means in terms of the variables. Complete your work in the space provided.

Answer 1

By defining the ones digit as x, we establish that the tens digit is 2x. The sum of the digits gives the equation x + 2x = 12, which solves to x = 4. The number is then 84, satisfying the problem's conditions.

Step-by-step explanation:

The problem requires finding a two-digit number based on the two given conditions: the tens digit is twice the ones digit, and the sum of the two digits is 12.

• Let the ones digit be represented by the variable x. Thus, the tens digit, which is twice the ones digit, can be represented as 2x.
• With the condition that the sum of the digits is 12, we can express this as an equation: x + 2x = 12.
• Solving this equation, we get 3x = 12, which simplifies to x = 4. Therefore, the ones digit is 4 and the tens digit is 2 times 4, which is 8.
• The two-digit number is therefore 84.

The solution means that the ones digit of the number is 4 and the tens digit is 8, satisfying both conditions of the problem.