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(52750)   (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.