Problem: Find the values of p and q, given (3 2p) and (5 3q) are the digits in the thousands and tens places respectively of the number 84527.

Solution:

Step 1: Write the number in expanded form.
84527 = 80000 + 4000 + 500 + 20 + 7

Step 2: Identify the digits in the thousands and tens places.
Thousands digit: 3 2p
Tens digit: 5 3q

Step 3: Replace the thousands and tens digits with their respective values.
80000 + 4000p + 500 + 30q + 7 = 84527

Step 4: Simplify and solve for p and q.
Combining like terms, we get:
84000 + 4000p + 30q = 84520
Dividing both sides by 10, we get:
8400 + 400p + 3q = 8452
Subtracting 8400 from both sides, we get:
400p + 3q = 52
We know that p and q are digits, so they must be integers between 0 and 9. We can use trial and error to find the values that satisfy the equation:
If p = 1, then 400 + 3q = 52, which is not possible since 3q must be a multiple of 3.
If p = 2, then 800 + 3q = 52, which is not possible since 3q must be a multiple of 3.
If p = 3, then 1200 + 3q = 52, which is not possible since 3q must be a multiple of 3.
If p = 4, then 1600 + 3q = 52, which is not possible since 3q must be a multiple of 3.
If p = 5, then 2000 + 3q = 52, which is not possible since 3q must be a multiple of 3.
If p = 6, then 2400 + 3q = 52, which is not possible since 3q must be a multiple of 3.
If p = 7, then 2800 + 3q = 52, which is not possible since 3q must be a multiple of 3.
If p = 8, then 3200 + 3q = 52, which is not possible since 3q must be a multiple of 3.
If p = 9, then 3600 + 3q = 52, which gives q = 4.
Therefore, p = 9 and q = 4.

Answer: p = 9 and q = 4.

Ans is 0.5, -1