Question

the sum of two numbers is 25. one number is twice the second number plus seven. what are the two numbers?

Explanation:

Step1: Define variables

Let the second number be \( x \). Then the first number is \( 2x + 7 \).

Step2: Set up equation

The sum of the two numbers is 25, so \( x+(2x + 7)=25 \).

Step3: Solve the equation

Simplify the left side: \( 3x+7 = 25 \).
Subtract 7 from both sides: \( 3x=25 - 7=18 \).
Divide both sides by 3: \( x=\frac{18}{3}=6 \).

Step4: Find the first number

Substitute \( x = 6 \) into \( 2x + 7 \): \( 2\times6+7 = 12 + 7=19 \).

Answer:

The two numbers are 6 and 19.