SOLUTION: If the larger of two numbers is divided by a smaller , the quotient and remainder are 2 each . If 5 times the smaller number is divided by , the larger ,the quotient and remainder

Question 191913: If the larger of two numbers is divided by a smaller , the quotient and remainder are 2 each . If 5 times the smaller number is divided by , the larger ,the quotient and remainder are still to each . Find the two numbers.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If the larger of two numbers is divided by a smaller , the quotient and remainder are 2 each .
:
Two numbers x & y, (x is the largest)
If we subtract the remainder from the problem, we get the even quotient
- = 2
simplify, multiply equation by y
x - 2 = 2y
x = (2y+2)
:
If 5 times the smaller number is divided by, the larger,the quotient and remainder are still to each .
- = 2
simplify the same way, multiply by x
5y - 2 = 2x
;
Find the two numbers
:
Substitute (2y+2) for x in the above equation
5y - 2 = 2(2y+2)
5y - 2 = 4y + 4
5y - 4y = 4 + 2
y = 6
:
Find x using x = 2y + 2
x = 2(6) + 2
x = 14
;
The numbers are 14 & 6
:
See if that is true using the statement:
"5 times the smaller number is divided by the larger, the quotient and remainder are still 2"
=
gives quotient of 2 and a remainder of 2

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