In a chemistry lab, there are 9.52 grams of a powdered substance in a container. Max needs to place an equal amount of the powdered substance into each of 3 glass plates. The amount of powdered substance he places into each glass plate is 1.98 grams.

Max estimates that there are about 4.5 grams of the powdered substance remaining in the container. Is his statement reasonable?
A.
This is reasonable because 9.52 grams can be rounded to 9 grams and 1.98 grams can be rounded to 1.5 grams. Since 9 − 3(1.5) = 4.5, there would be about 4.5 grams of the powdered substance remaining in the container.
B.
This is not reasonable because 9.52 grams can be rounded to 9.5 grams and 1.98 grams can be rounded to 2 grams. Since 9.5 − 3(2) = 3.5, there would be about 3.5 grams of the powdered substance remaining in the container.
C.
This is reasonable because 9.52 grams can be rounded to 9 grams and 1.98 grams can be rounded to 2.5 grams. Since 9 − 3(2.5) = 1.5, there would be about 1.5 grams of the powdered substance remaining in the container.
D.
This is not reasonable because 9.52 grams can be rounded to 9 grams and 1.98 grams can be rounded to 1 gram. Since 9 − 3(1) = 6, there would be about 6 grams of the powdered substance remaining in the container.

1 answer

To evaluate Max's estimate of the amount of powdered substance remaining in the container, let's first do the calculations based on the actual values.

  1. Max has 9.52 grams in total.
  2. He places 1.98 grams into each of the 3 glass plates.

Calculating the total amount he removes: \[ 3 \times 1.98 = 5.94 \text{ grams} \]

Now, calculating the remaining amount in the container: \[ 9.52 - 5.94 = 3.58 \text{ grams} \]

Now let’s check Max's estimate of 4.5 grams against the rounding arguments in the provided options.

Evaluating Each Option:

Option A:

  • Rounding 9.52 to 9 and 1.98 to 1.5: \[ 9 - 3(1.5) = 9 - 4.5 = 4.5 \] This calculation is correct according to this rounding.

Option B:

  • Rounding 9.52 to 9.5 and 1.98 to 2: \[ 9.5 - 3(2) = 9.5 - 6 = 3.5 \] This is not close to 4.5 grams.

Option C:

  • Rounding 9.52 to 9 and 1.98 to 2.5: \[ 9 - 3(2.5) = 9 - 7.5 = 1.5 \] This does not support Max's estimate of 4.5 grams.

Option D:

  • Rounding 9.52 to 9 and 1.98 to 1: \[ 9 - 3(1) = 9 - 3 = 6 \] This is also far from 4.5 grams.

Conclusion:

The only option supporting Max's estimate is Option A, where rounding yields a computation leading to approximately 4.5 grams remaining. Therefore, it can be concluded that Max's estimate is reasonable based on that rounding.

The correct choice is: A. This is reasonable because 9.52 grams can be rounded to 9 grams and 1.98 grams can be rounded to 1.5 grams. Since 9 − 3(1.5) = 4.5, there would be about 4.5 grams of the powdered substance remaining in the container.