Question

the sum of three numbers is 100. the third number is 3 times the second. the first number is 10 less than the second. 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 \( x - 10 \), and the third number is \( 3x \).

Step2: Set up equation

The sum of the three numbers is 100, so \((x - 10) + x + 3x = 100\).

Step3: Simplify equation

Combine like terms: \( 5x - 10 = 100 \).

Step4: Solve for x

Add 10 to both sides: \( 5x = 110 \). Divide by 5: \( x = 22 \).

Step5: Find other numbers

First number: \( 22 - 10 = 12 \). Third number: \( 3 \times 22 = 66 \).

Answer:

First number: 12, Second number: 22, Third number: 66