SOLUTION: 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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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) About Me  (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
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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) About Me  (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:

5n=3%28n%2B2%29%2B54

5n=3n%2B6%2B54

5n=3n%2B60

Subtract 3n from both sides of the equation

5n-3n=3n%2B60-3n

2n=60

Divide by 2 to both sides of the equation yields

2n%2F2=60%2F2

n=30 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.

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Good luck in your studies!

Respectfully,
Dr J