Question

1. three times a number added to another number is 18. two times the first number minus the other number is 2. what is the sum of the two numbers?

Explanation:

Step1: Define variables

Let the first number be \( x \) and the second number be \( y \).

Step2: Set up equations

From the problem, we have:
\( 3x + y = 18 \) (Equation 1)
\( 2x - y = 2 \) (Equation 2)

Step3: Solve the system of equations

Add Equation 1 and Equation 2 to eliminate \( y \):
\( (3x + y) + (2x - y) = 18 + 2 \)
\( 3x + y + 2x - y = 20 \)
\( 5x = 20 \)
\( x = 4 \)

Step4: Find the value of \( y \)

Substitute \( x = 4 \) into Equation 1:
\( 3(4) + y = 18 \)
\( 12 + y = 18 \)
\( y = 18 - 12 \)
\( y = 6 \)

Step5: Find the sum of the two numbers

The sum of \( x \) and \( y \) is \( x + y = 4 + 6 = 10 \)

Answer:

10