SOLUTION: the reduced fraction m/n is less than 1/5 and m+n=100 find the greatest possible such fraction

Algebra.Com
Question 1140817: the reduced fraction m/n is less than 1/5 and m+n=100 find the greatest possible such fraction
Found 3 solutions by ankor@dixie-net.com, ikleyn, greenestamps:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
the reduced fraction m/n is less than 1/5 and m+n=100
find the greatest possible such fraction.
m + n = 100
m = -n + 100
therefore:
<
cross multiply, reverse the inequality
n >
n > -5n + 500
n + 5n > 500
6n > 500
n > 500/6
n > 83.333
n = 84 the nearest integer that satisfies this
therefore
is the greatest possible fraction
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.

            The answer    =   which tutor @ankor found,   is not the solution to the problem,

            since the fraction    is not reduced.  I came to bring the correct answer and solution. 


m + n = 100   ====>  n = 100-m.


So the inequality   <    takes the form


     < 

    5m < 100 - m

    6m < 100

    m  <  = 16.66...

    m <= 16.


Now we should consider all the fractions    with  0 <= m <= 16 and select maximal of that which IS REDUCED.


I did it using EXCEL.  See the table below.



      T   A   B   L   E   


m     100-m      -reduced or not    Value of 


16	84	    No	
15	85	    No	
14	86	    No	
13	87	    Yes                          0.149425287   <<<---===  The maximum value :  the solution and the answer
12	88	    No	 
11	89	    Yes	                         0.123595506
10	90	    No	 
9	91	    Yes	                         0.098901099
8	92	    No	 
7	93	    Yes	                         0.075268817
6	94	    No	
5	95	    No	
4	96	    No	
3	97	    Yes	                         0.030927835
2	98	    No	
1	99	    Yes	                         0.01010101


ANSWER.  The greatest possible such fraction is   = 0.149425287.

Solved, answered, explained and completed.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


m/n < 1/5 and m+n=100 means






Since m is an integer, the maximum possible value for m is 16.

To maximize the value of m/n, with the requirement that m+n=100, m must be as large as possible. So the possible values we need to look at for m are 16, 15, 14, ....

If m is even, then n=100-m will also be even, and m/n will not be a reduced fraction.

If m is a multiple of 5, then n=100-m will also be a multiple of 5, and m/n will not be a reduced fraction.

So m can't be 16, 15, or 14. So

m=13 --> n = 87

The largest fraction that satisfies the conditions of the problem is

m/n = 13/87
RELATED QUESTIONS

1. Find the measures of two complementary angles, (answered by rfer)
Simplify the complex fraction completely: (9 - m^2 n^-2) ÷ (3 - m^1... (answered by josgarithmetic)
if m and n are prime numbers such that the sum of m and n is greater than 20 and the... (answered by Fombitz)
A fraction is such that whose numerator is a 4 less than the denominator. If 1 is... (answered by ankor@dixie-net.com)
Find the measures of two complementary angles, (answered by cleomenius)
Find the measures of two supplementary angles, N and M if the measure of angle N is 5... (answered by cleomenius)
find the measure of two supplementary angles, N and M, if the measure of angle N is 5... (answered by Boreal)
if m and n are whole numbers not equal to zero, explain how m and n are related. 1)... (answered by chessace,richard1234)
find three points M,N and P such that m(M,N)=1/2 , m(M,P)=5 and... (answered by drk)