SOLUTION: Hello, I need help please! The question is Find two consecutive odd integers such that six more than nine times the first integer is five times the second integer. Find the integ

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Question 156696: Hello, I need help please! The question is Find two consecutive odd integers such that six more than nine times the first integer is five times the second integer. Find the integers. Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Consecutive odd integers are integers that are odd and are next to one another. So numbers like 1,3,5,7,etc are consecutive odd integers. Algebraically, they follow the form 2x%2B1, 2x%2B3, 2x%2B5, etc. where "x" is any integer.


Also, because "six more than nine times the first integer is five times the second integer", this translates to 9%282x%2B1%29%2B6=5%282x%2B3%29 where 2x%2B1 is the first number and 2x%2B3 is the second number





9%282x%2B1%29%2B6=5%282x%2B3%29 Start with the given equation.


18x%2B9%2B6=10x%2B15 Distribute.


18x%2B15=10x%2B15 Combine like terms on the left side.


18x=10x%2B15-15 Subtract 15 from both sides.


18x-10x=15-15 Subtract 10x from both sides.


8x=15-15 Combine like terms on the left side.


8x=0 Combine like terms on the right side.


x=%280%29%2F%288%29 Divide both sides by 8 to isolate x.


x=0 Reduce.


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2x%2B1 Now move onto the expression for the first number


2%280%29%2B1 Plug in x=0.


0%2B1 Multiply 2 and 0 to get 0.


1 Combine like terms.


So the first number is 1.



2x%2B3 Now move onto the expression for the second number


2%280%29%2B3 Plug in x=0.


0%2B3 Multiply 2 and 0 to get 0.


3 Combine like terms.


So the second number is 3.


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Answer:


So the two numbers are 1 and 3


Check:

9%281%29%2B6=5%283%29


9%2B6=15


15=15 works.