Question

the sum of three numbers is 103. the first number is 7 less than the second. the third number is 2 times the first. what are the numbers? first number: second number: third number:

Explanation:

Step1: Define variables

Let the second number be \( x \). Then the first number is \( x - 7 \), and the third number is \( 2(x - 7) \).

Step2: Set up the equation

The sum of the three numbers is 103, so:

$$ (x - 7) + x + 2(x - 7) = 103 $$

Step3: Simplify the equation

First, expand and combine like terms:

$$ x - 7 + x + 2x - 14 = 103 $$

$$ 4x - 21 = 103 $$

Step4: Solve for \( x \)

Add 21 to both sides:

$$ 4x = 103 + 21 $$

$$ 4x = 124 $$

Divide both sides by 4:

$$ x = \frac{124}{4} = 31 $$

Step5: Find the other numbers

First number: \( x - 7 = 31 - 7 = 24 \)
Third number: \( 2(x - 7) = 2 \times 24 = 48 \)

Answer:

First number: 24
Second number: 31
Third number: 48