The difference of two numbers is 62, and the sum of twice the larger and three times the smaller is 304. Find the two numbers.

Mathematics · College · Mon Jan 18 2021

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given that, difference of two numbers is 62 and the sum of twice the larger and three times the smaller is 304 .

let the larger number be x and smaller number is y so now:-

​​xy  =62    (difference of numbers)

x =62+y ……(1)​

and

2x+3y = 304 ……(2)          ( sum of twice the larger and three times the smaller number)

Find the value of x and y.

Substitute the value of x from equation (1) in equation (2).

=> 2(62+y)+3y=304

=> 124+2y+3y=304

=> 5y=180

=> y=36

Substitute the value of y in equation (1)

x=36+62 

  =98​

Therefore, the two numbers are 36 and 98 respectively.

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