Three nos are in the ratio 3:4:5 . If the sum of the largest and the smallest equals the sum of the third and 52. Find the numbers ?

3 Answers
Dec 3, 2016

The numbers are 39, 52 and 65

Explanation:

The numbers are 3n,4n and 5n
We just need to find whether 3,4,5 or 6,8,10, or 9,12,15 etc
So 3n +5n= 4n+52
Simplify
8n=4n+52
Solve
4n=52
n=13
The 3 numbers are 39:52:65

Dec 3, 2016

39,52 and 65

Explanation:

There should be new triangle for propionate to 3:4:5
Let take x and multiple it to 3:4:5 to make new triangle
3x+5x=4x+523x+5x=4x+52
3x+5x-4x=523x+5x4x=52
or
4x=524x=52
or
x=52/4x=524
or
x=13x=13

Put the value of x =13 in 3x+5x=4x+523x+5x=4x+52
3*13+5*13=4*13+52313+513=413+52
or
39+65 = 52+5239+65=52+52

or
104 = 104104=104

Hence the numbers are 39,52 and 65

Dec 3, 2016

39 : 52 : 65

color(red)("There is ambiguity in this question.")There is ambiguity in this question.

Explanation:

Consider the ratios

We have 3 parts, 4 parts and finally 5 parts. This gives a total of 12 parts

Let the first number be aa
Let the second number be bb
Let the third number be cc

Let the sum of all the numbers be ss

So we have:

a" : "b" : "c" " =" " 3" : "4" : "5a : b : c = 3 : 4 : 5

3 parts < 4 parts < 5 parts so " " a < b < c a<b<c and a+b+c=sa+b+c=s
the first number is a=3/12sa=312s

the second number is b=4/12sb=412s

the third number is c=5/12sc=512s
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Lets break down the wording of the question:

The sum of the largest and the smallest: " "-> a+c a+c
equals:" "->a+c=? a+c=?
the sum of:" "->a+c=?+? a+c=?+?
the third:" "->a+c=c+ a+c=c+
and 52: " "->a+c=c+52 a+c=c+52

color(red)("This configuration points to "a=52)This configuration points to a=52

color(green)("There is no point in continuing until this approach is confirmed as ok")There is no point in continuing until this approach is confirmed as ok

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~color(magenta)("Possible error in the question")Possible error in the question~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

color(magenta)("The line:")The line:

color(magenta)("the third: "->a+c=c+ the third: a+c=c+

color(green)("Should read:")Should read:
color(green)("the second: "->a+c=b+ )the second: a+c=b+

color(green)("or")or
color(green)("the middle: "->a+c=b+ )the middle: a+c=b+
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Solving for : "a+c=b+52)Solving for : a+c=b+52

By substitution we have:

3/12s+5/12s=4/12s+52312s+512s=412s+52

8/12s-4/12s=52812s412s=52

1/3s=5213s=52

=> s= 156s=156

a=1/4xx156=39a=14×156=39
b=1/3xx156=52b=13×156=52
c=5/12xx156=65c=512×156=65