SOLUTION: The sum of three numbers is 123. The second number is 9 less than two times the first number. The third number is 6 more than three times the first number. Find the three number

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Question 228836: The sum of three numbers is 123. The second number is 9 less than two times the first number. The third number is 6 more than three times the first number. Find the three numbers. Thank you very much.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of three numbers is 123. The second number is 9 less than two times the first number. The third number is 6 more than three times the first number. Find the three numbers. Thank you very much.

Step 1. Let n be the first number.

Step 2. Let 2n-9 be the second number since it is 9 less than two times the first number.

Step 3. Let 3n+6 be the third number since it is 6 more than three times the first number.

Step 4. Then n+2n-9+3n+6=123 since their sum is 123.

Step 5. Solving n+2n-9+3n+6=123 yields the following steps

6n-3=123

Add 3 to both sides of the equation

6n-3%2B3=123%2B3%5D%5D%5D%0D%0A%0D%0A%0D%0A%7B%7B%7B6n=126

Divide by 6 to both sides of equation

6n%2F6=126%2F6

n=21 2n-9=42-9=33 and 3n%2B6=63%2B6=69.

Note the above numbers should add up to 123: 21+33+69=123...which it does.

Step 6. ANSWER: The numbers are 21,33, and 69.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J