Question 81470: the sum of two numbers is 23.twice the larger number is 4 more than 4 times the smaller.what are the numbers?
Answer by praseenakos@yahoo.com(507)   (Show Source):
You can put this solution on YOUR website! 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,
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