# 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

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

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

or

or

or

Put the value of x =13 in

or

or

Hence the numbers are 39,52 and 65

39 : 52 : 65

#### 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

Let the second number be

Let the third number be

Let the sum of all the numbers be

So we have:

3 parts < 4 parts < 5 parts so

the first number is

the second number is

the third number is

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Lets break down the wording of the question:

The sum of the largest and the smallest:

equals:

the sum of:

the third:

and 52:

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By substitution we have: