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?

type a response

Explanation:

Step1: Define variables

Let the first number be \( x \) and the second number be \( y \). From the problem, we have two equations:

1. \( 3x + y = 18 \) (Three times a number added to another number is 18)
2. \( 2x - y = 2 \) (Two times the first number minus the other number is 2)

Step2: Solve the system of equations

We can add the two equations together to eliminate \( y \).
\( (3x + y) + (2x - y) = 18 + 2 \)
Simplifying the left - hand side: \( 3x + y+2x - y=5x \)
Simplifying the right - hand side: \( 20 \)
So, \( 5x = 20 \)
Divide both sides by 5: \( x=\frac{20}{5}=4 \)

Step3: Find the value of \( y \)

Substitute \( x = 4 \) into the first equation \( 3x + y = 18 \)
\( 3\times4 + y=18 \)
\( 12 + y = 18 \)
Subtract 12 from both sides: \( y=18 - 12 = 6 \)

Step4: Find the sum of the two numbers

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

Answer:

10