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Question 622627: If the sum of nine consecutive integers is 108, what is the smallest of the nine numbers?
the answer choices are either 6, 8, 9, 10, or 12. Please explain how to solve and thank you!
Found 2 solutions by math-vortex, Alan3354:
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! Hi, there--
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Consecutive integers are numbers in counting order. For example, 2, 3, 4, 5, ... are consecutive integers. Integers also include zero and negative numbers, but your list of possible answers does not allow for that.
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One way you can solve this problem is to test the possible answers until you find the right one. Suppose you decide to test the integer 10. You add nine consecutive integers beginning with 10 (10+11+12+...+18) and find their sum. If the sum is too high, try a smaller number. This guess and check method is a viable math strategy, but it can take time.
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Here is an algebra way to solve the problem.
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Let x be the smallest of the nine numbers.
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Then the next eight consecutive integers are x+1, x+2, x+3, x+4, x+5, x+6, x+7, and x+8.
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We know that the sum of these integers is 108. In algebra, we write this as the equation,
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Now we simplify this equation by combining like terms and solving for x.
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Subtract 36 from both sides of the equation.
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Divide both sides of the equation by 9.
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In the context of this problem, x=8 means that the smallest of the nine numbers is 8.
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We should check our answer to see if it works.
8+9+10+11+12+13+14+15+16=108 Check!
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Feel free to email me if there is a part that you sell have questions about.
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Ms.Figgy
math.in.the.vortex@gmail.com
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! If the sum of nine consecutive integers is 108, what is the smallest of the nine numbers?
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108/9 = 12, the middle number
--> 4 below 9, 9, and 4 above 9
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