Question 126446
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.