SOLUTION: If the larger of two numbers is divided by the smaller, the quotient is 7 and the remainder is 19. But if 3 times the greater is divided by twice the smaller, the quotient is 11 an

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Question 1097559: If the larger of two numbers is divided by the smaller, the quotient is 7 and the remainder is 19. But if 3 times the greater is divided by twice the smaller, the quotient is 11 and the remainder is 19. What are the numbers?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Let x be the larger of the two numbers and y be the smaller.

Then the condition gives you these two equations


x = 7y + 19,           (1)

3x = 11*(2y) + 19.     (2)


Substitute (1) into (2). You will get


3*(7y + 19) = 22y + 19,    or

21y + 57 = 22y + 19  ====>  y = 57 - 19 = 38.


Then  x = 7*y + 19 = 7*38 + 19 = 285.


Answer.  The larger number is 285.  The smaller number is 38.


Check.   Check eq(1):  7*y+19 = 7*38+19 = 285 = x.             ! Correct !

         Check eq(2):  3x = 3*285 = 11*2*38+19 = 11*(2x)+19.   ! Correct !


Thanks to @MathTherapy for pointing my error in the earlier version.



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

If the larger of two numbers is divided by the smaller, the quotient is 7 and the remainder is 19. But if 3 times the greater is divided by twice the smaller, the quotient is 11 and the remainder is 19. What are the numbers?
 

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