SOLUTION: The differance between two numbers is 15. When twice the smaller number is subtracted from three times the larger number, the difference is 58. What is the larger number?

Question 126446: The differance between two numbers is 15. When twice the smaller number is subtracted from three times the larger number, the difference is 58. What is the larger number?
Answer by praseenakos@yahoo.com(507) (Show Source): You can put this solution on YOUR website!
Question:
The differance between two numbers is 15. When twice the smaller number is subtracted from three times the larger number, the difference is 58. What is the larger number?

Answer:
Assume that the larger number is 'x' and the smaller number is 'y'
It is given that, The differance between two numbers is 15

==> x-y = 15 -------(1)

==> y = x-15 --------(2)

twice the smaller number = 2y

Three times the larger number = 3x

When twice the smaller number is subtracted from three times the larger number, the difference is 58....means
==> 3x - 2y = 58-------(3)

substitute the value, y = x-15 in the third equation...

==> 3x - 2(x-15) = 58

==> 3x - 2x + 30 = 58

==> x + 30 = 58

subtract 30 from both sides....

==> x + 30 - 30 = 58 - 30

==> x = 28

So the value of y = x - 15 = 28 - 15 = 13

So the larger number is 28 and the smaller number is 13

Hope you found the explanation useful.

Regards.

Praseena.

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