SOLUTION: there are 3 consecutive even integers. When the least is divided by 4, the next by 5, and the greatest by 9, the sum of the quotients is 39. What are the numbers?

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: there are 3 consecutive even integers. When the least is divided by 4, the next by 5, and the greatest by 9, the sum of the quotients is 39. What are the numbers?      Log On


   

Question 1014594: there are 3 consecutive even integers. When the least is divided by 4, the next by 5, and the greatest by 9, the sum of the quotients is 39. What are the numbers?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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S=smallest; M=middle=S+2; L=largest=S+4
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%28S%2F4%29%2B%28M%2F5%29%2B%28L%2F9%29=39
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%28S%2F4%29%2B%28%28S%2B2%29%2F5%29%2B%28%28S%2B4%29%2F9%29=39
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45S%2F180%2B%2836%28S%2B2%29%29%2F180%2B%2820%28S%2B4%29%29%2F180=39
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45S%2B%2836S%2B72%29%2B%2820S%2B80%29=7020
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101S%2B152=7020
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101S=6868
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S=68
ANSWER 1: The smallest number is 68.
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M=S%2B2=68%2B2=70
ANSWER 2: The middle number is 70.
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L=S+4=68+4=72
ANSWER 3: The largest number is 72.
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CHECK:
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%28S%2F4%29%2B%28M%2F5%29%2B%28L%2F9%29=39
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%2868%2F4%29%2B%2870%2F5%29%2B%2872%2F9%29=39
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17%2B14%2B8=39
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39=39
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