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

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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