Question

1. twice a number added to another number is 15. the sum of the two numbers is 11. find the 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 two equations:

1. \( 2x + y = 15 \) (Twice a number added to another number is 15)
2. \( x + y = 11 \) (The sum of the two numbers is 11)

Step3: Subtract the second equation from the first

\( (2x + y) - (x + y) = 15 - 11 \)
Simplify the left side: \( 2x + y - x - y = x \)
Simplify the right side: \( 4 \)
So, \( x = 4 \)

Step4: Find the value of \( y \)

Substitute \( x = 4 \) into the second equation \( x + y = 11 \)
\( 4 + y = 11 \)
Subtract 4 from both sides: \( y = 11 - 4 = 7 \)

Answer:

The two numbers are 4 and 7.