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

Answer:

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

Answer:

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

Answer:

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#