SOLUTION: Find two consecutive odd integers such that three-fourths of the larger number is 5 more than one-fourth of the smaller number. Find the numbers.

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Find two consecutive odd integers such that three-fourths of the larger number is 5 more than one-fourth of the smaller number. Find the numbers.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 785464: Find two consecutive odd integers such that three-fourths of the larger number is 5 more than one-fourth of the smaller number. Find the numbers.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I do not care that if two numbers in a problem are both odd or both even. Either way the difference between the numbers would be 2.
I just find pairs of numbers, both odd or both even, that satisfy the conditions of the problem.
If the solution found does not match the parity (odd or even) required by the problem, then there is no solution to the problem. (That could happen in a real life problem, but math class problems bear little resemblance to real life, so if I find only even solutions here I will recheck my calculations)
n= the smaller odd integer
n%2B2= the next (larger) odd integer

What the problem says in words translates as
%283%2F4%29%28n%2B2%29=%281%2F4%29n%2B5 or 3%28n%2B2%29%2F4=n%2F4%2B5
Multiplying times 4 to eliminate denominators, we get
3%28n%2B2%29=n%2B5%2A4
3n%2B6=n%2B20
3n%2B6-n=20
3n-n=20-6
2n=14
n=14%2F2
highlight%28n=7%29 --> n%2B2=7%2B2 --> highlight%28n%2B2=9%29
My solution has odd numbers, so it is a valid solution.