SOLUTION: One-fourth of a number is greater than one-fifth of the number succeeding it by 1. Find the number. a) 24 b) 42 c) 36 d) 48

Algebra ->  Expressions -> SOLUTION: One-fourth of a number is greater than one-fifth of the number succeeding it by 1. Find the number. a) 24 b) 42 c) 36 d) 48      Log On


   

Question 1055619: One-fourth of a number is
greater than one-fifth of the number
succeeding it by 1. Find the number.
a) 24 b) 42 c) 36 d) 48
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The difficulty is in understanding what the wording of the problem means.
Since it is a multiple choice question, once you understand what it means,
all you need to know is basic arithmetic, and trial and error.

ARITHMETIC:
Trying to see if 24 is the answer:
One-fourth of 24 is 6 (24 divided by 4).
The number succeeding it (the number after 24) is 25.
One-fifth of 25 is 5 (25 divided by 5).
Is 6 greater than 5 by 1?
Let's see,
6-5=1 ,
so 6 is indeed greater than 5 by one,
and highlight%2824%29 is a possible solution to the problem.
It must be THE one and only solution,
because we had to choose one of the four choices given.
We do not need to try the other choices.

THE ALGEBRA WAY:
n= the number
n%2B1= the number succeeding it
n%2F4= one-fourth of the number
The wording means that n%2F4 is 1 more than
%28n%2B1%29%2F5 .
The equation is
n%2F4=%28n%2B1%29%2F5%2B1
To get rid of denominators,
we could multiply both sides of the equal sign times 4 and times 5,
or we could just multiply both sides time 4%2A5=20 in a single step.
20%2A%28n%2F4%29=20%2A%28%28n%2B1%29%2F5%2B1%29
20n%2F4=20%28n%2B1%29%2F5%2B20
5n=4%28n%2B1%29%2B20
5n=4n%2B4%2B20
5n=4n%2B24
5n-4n=24
highlight%28n=24%29