we have to make a two equation and thenn solve it step by step

Question

if the larger of the numbers is divided by the smaller, the quotient and the reminder are 2 each. if 5 times asmaller number is divided by the larger, the quotient and the reminder are still 2 each. find the two numbers.

Answer 1

Usama,

 

Forget for a moment that the quotient is 2 and consider a more general solution such that:

 

Let x = larger number and y = smaller number, and Q = quotient.

 

Then x÷y = Q   (+2 remainder)

 

and 5y÷x = Q   (+2 remainder)

 

we can rewrite these as x = Qy  (+2 remainder)  so  x = Qy + 2

and                            5y = Qx  (+2 remainder)  so 5y = Qx +2

 

No replace Q with the value of the quotient Q = 2 and our two equations become:

 

x = 2y + 2

5y = 2x + 2

 

substituting for x in the 2nd equation gives:

 

5y = 2(2y + 2) + 2 = 4y + 4 +2 = 4y + 6

 

5y - 4y = y = 6

 

So y = 6 then x = 14 

 

Check:  x/y = 14/6 = 2 + (remainder 2)

 

(5·y)/x = 30/14 = 2 + (remainder 2)