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+52
3x+5x4x=52
or
4x=52
or
x=524
or
x=13

Put the value of x =13 in 3x+5x=4x+52
313+513=413+52
or
39+65=52+52

or
104=104

Hence the numbers are 39,52 and 65

Dec 3, 2016

39 : 52 : 65

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 a
Let the second number be b
Let the third number be c

Let the sum of all the numbers be s

So we have:

a : b : c = 3 : 4 : 5

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

the second number is b=412s

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

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

This configuration points to a=52

There is no point in continuing until this approach is confirmed as ok

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~Possible error in the question~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The line:

the third: a+c=c+

Should read:
the second: a+c=b+

or
the middle: a+c=b+
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solving for : a+c=b+52

By substitution we have:

312s+512s=412s+52

812s412s=52

13s=52

s=156

a=14×156=39
b=13×156=52
c=512×156=65