Question 81470
QUESTION:



the sum of two numbers is 23.twice the larger number is 4 more than 4 times the smaller.what are the numbers?



ANSWERS:


Assume that the larger number is 'x' and the smaller number is 'y'


Given that their sum is = 23




==> x + y = 23  --------------------(1)


Twice the largerr number cam be expressed as '2x'


four times the smaller number can be expressed as, '4x'



twice the larger number is 4 more than 4 times the smaller can be expressed as,



==>  2x = 4y + 4



==> 2x - 4y = 4 -----------------(2)




Multiply (1) throughout with 4




==> 4(x + y) = 4 * 23 



==> 4x + 4y = 92 ---------------(3)


Now add (2) and (3)


2x - 4y = 4 -----------------(2)

4x + 4y = 92 ---------------(3)



==> 2x - 4y + 4x + 4y = 4 + 92



==>  6x = 96



Divide throughout by 6



==> 6x/6 = 96/6



==> x = 16



Now substitute this value of x in the given condition, x + y = 23



==> 16 + y = 23


Subtract 16 from both sides



==> 16 + y - 16 = 23 - 16



==> y = 7



So the larger number is 16and the smaller number is 7.




Hope you found the explanation useful.



Regards.



Praseena,