Question 539814: Using Equations to solve Problems.
The sum of 3 numbers is 39. The second number is three times the first. The third number is 4 more than the first. What are th three numbers? *Must show all work*
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Call the three numbers a, b, and c. (a is the first number, b is the second, and c is the third.)
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The problem tells you that the sum of the three numbers is 39. In equation form this is written as:
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The problem tells you that the second number (that is b) is three times the first number (a). So b equals 3a. Therefore, you can substitute 3a for b in the equation for the sum of the three numbers. This replacement changes the equation to:
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The problem also tells you that the third term (c) is 4 more than the first term (a). In other words, c is equal to a + 4. This means that you can substitute a + 4 for c in the above equation. When you do that the equation becomes:
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This equation only has one unknown and it can be solved for that unknown. Begin by combining all the terms that contain the unknown a. Do that by adding a, 3a, and a to get a total of 5a. The equation then becomes:
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Next get rid of the +4 on the left side by subtracting 4 from both sides to get:
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Finally, solve for a by dividing both sides by the 5 that multiplies the a. Dividing both sides by 5 results in:
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So you now know that the first number you are looking for is 7. The second number has to be 3 times that so it is 3 times 7 or 21. And the third number is 4 more than the first number, so it is 7 + 4 or 11.
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The three numbers for the answer are 7, 21, and 11. If you add them you will find that they do total 39. Also one of them is 3 times the first number, and one is 4 more than the first number. So the answer checks because it satisfies everything given as criteria in the problem.
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Hope this helps you to understand the problem.
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