Question 18

Explanation

Given information from the question:

• Initial barn stock = $55$ tons.
• Daily harvest ($x$) ranges between $0.04$ and $0.09$ tons.
• $P = 55$ tons.
• $Q =$ Total rice collected after $8$ days.

Calculating Quantity Q

The total rice in the barn ($Q$) is the initial stock plus the harvest collected over $8$ days.

We calculate the range of additional rice from harvesting for $8$ days:

• Minimum additional: $8 \times 0.04 = 0.32$ tons.
• Maximum additional: $8 \times 0.09 = 0.72$ tons.

Thus, the range for the total rice ($Q$) is:

Comparing P and Q

Now we compare the values of $P$ and $Q$:

• $P = 55$
• $Q$ is at least $55.32$

Since the minimum value of $Q$ ($55.32$) is already greater than $P$ ($55$), it is certain that $Q$ is always greater than $P$.

So, the correct relationship is $P < Q$.