Question

the sum and difference of two numbers are in the ratio 19:7,what are the numbers.(please explain)​

Answer 1

Step-by-step explanation:

let the numbers are x and y

so,

(x+y) : (x-y)= 19 : 7

=> (x+y)/(x-y)= 19/7

=> 7(x+y)=19(x-y)

=> 7x+7y=19x-19y

=> 7x-19x= -19y-7y

=> -12x= -26y

=> x/y= -26/-12

=> x/y=13/6

=> x : y= 13 : 6

so the ratio of the numbers is

13 : 6

Answer 2

Given :-

$a+b:a-b=19:7$

Required to find :-

$a=?\\b=?$

Approach :-

Let us equate the ratios to form 2 equations.

$a+b=19$  ---------- 1

$a-b=7$  ----------- 2

Let us add 1 and 2

$2a=26\\a=13$

Now let us substitute in 2

$13-b=7\\6=b$

∴ The numbers whose ratio of sum to the difference of them are 19:7 is 13 and 6.