SOLUTION: if x is divided by y, the quotient if 8 and the remainder if 3. If 8 is divided by z, the quotient is 4 and the remainder is 1. If x is divided by yz, the remainder is y+3. What is

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Question 1102694: if x is divided by y, the quotient if 8 and the remainder if 3. If 8 is divided by z, the quotient is 4 and the remainder is 1. If x is divided by yz, the remainder is y+3. What is the quotient?
Found 3 solutions by Edwin McCravy, ikleyn, greenestamps:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!

I think there's a mistake, because of

If 8 is divided by z, the quotient is 4 and the remainder is 1.
So,

  4
z)8
  R=1

Since 

(quotient)(divisor)+(remainder) = (dividend)

That means that 
                
                

I think you meant for z to be an integer, not a fraction.

Edwin
Answer by ikleyn(52752)   (Show Source): You can put this solution on YOUR website!
.
The condition DEFINITELY is WRONG.


Answer by greenestamps(13195)   (Show Source): You can put this solution on YOUR website!


Normally, it would be expected that, when a problem talks about divisors, quotients, and remainders, the numbers are all integers. However, that need not be the case.

And if we allow non-integer values for the variables in this problem, we can get an answer.

If x is divided by y, the quotient is 8 and the remainder is 3.
translation: (1)
If 8 is divided by z, the quotient is 4 and the remainder is 1.
translation: (2)
If x is divided by yz, the remainder is y+3. What is the quotient?
translation: (3) where q is the quotient we are looking for

We can solve equation (2) to find z:




Equations (1) and (3) both give us expressions for x; set those two expressions equal to each other and see what we get:






The quotient we are looking for is 4.

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