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+5x-4x=52
or
4x=52
or
x=52/4
or
x=13

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

or
104 = 104

Hence the numbers are 39,52 and 65

Dec 3, 2016

39 : 52 : 65

color(red)("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=3/12s

the second number is b=4/12s

the third number is c=5/12s
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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

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

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

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

color(magenta)("The line:")

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

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

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

By substitution we have:

3/12s+5/12s=4/12s+52

8/12s-4/12s=52

1/3s=52

=> s= 156

a=1/4xx156=39
b=1/3xx156=52
c=5/12xx156=65