When an integer k is divided by -8, the quotient is 3. When 16 is divided by an integer p, the quotient is -8. What is the quotient when k is divided by p?
The correct answer and explanation is:
To solve this, we will break the problem down into two parts and then combine the results.
Part 1: Finding the value of kk
The problem tells us that when kk is divided by -8, the quotient is 3. This means: k−8=3\frac{k}{-8} = 3
Multiplying both sides of the equation by -8: k=3×(−8)=−24k = 3 \times (-8) = -24
So, k=−24k = -24.
Part 2: Finding the value of pp
Next, the problem states that when 16 is divided by pp, the quotient is -8. This means: 16p=−8\frac{16}{p} = -8
Multiplying both sides of the equation by pp: 16=−8p16 = -8p
Now, solving for pp: p=16−8=−2p = \frac{16}{-8} = -2
So, p=−2p = -2.
Part 3: Finding the quotient when kk is divided by pp
Now that we know k=−24k = -24 and p=−2p = -2, we can find the quotient when kk is divided by pp: kp=−24−2=12\frac{k}{p} = \frac{-24}{-2} = 12
Final Answer:
The quotient when kk is divided by pp is 12.
In conclusion, by applying the division relationships and solving for kk and pp, we determined that the quotient when kk is divided by pp is 12.