SOLUTION: Determine whether there are two consecutive odd integers such that 5 times the first exceeds 3 times the second by 54.

Question 221523: Determine whether there are two consecutive odd integers such that 5 times the first exceeds 3 times the second by 54.
Found 2 solutions by stanbon, drj:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Determine whether there are two consecutive odd integers such that 5 times the first exceeds 3 times the second by 54.
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1st odd: 2x-1
2nd odd: 2x+1
---------------------
Equations:
5(2x-1) = 3(2x+1)
10x-5 = 6x+3
4x = 8
x = 2
-------
1st odd: 2*2-1 = 3
2nd odd: 2*2+1 = 5
==========================
Cheers,
Stan H.
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Determine whether there are two consecutive odd integers such that 5 times the first exceeds 3 times the second by 54.

Step 1. Let n be the first odd integer.

Step 2. Let n+2 be then next consecutive odd integer.

Step 3. Let 5n be 5 times the first odd integer.

Step 4. Let 3(n+2) be 3 times the second odd integer.

Step 5. Then, 5n=3(n+2)+54 since 5 times the first exceeds 3 times the second by 54

Step 6. Solving the equation in Step 5 yields the following steps:

Subtract 3n from both sides of the equation

Divide by 2 to both sides of the equation yields

but n is an even integer.

Step 8. ANSWER: Therefore there are no odd integers that satisfies the given problem statement.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

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