Alright, let's go through the problem step-by-step.
1. Determine the Mass of Only the Crackers in the Box:
- First, we need to find out how much the crackers themselves weigh without the box.
- We know the total mass of the crackers and the box is 924 grams and the mass of the box alone is 328 grams.
- Therefore, the mass of the crackers is calculated as:
[tex]\[
\text{Mass of Crackers} = \text{Mass of Crackers + Box} - \text{Mass of Box}
\][/tex]
[tex]\[
\text{Mass of Crackers} = 924 \text{ grams} - 328 \text{ grams} = 596 \text{ grams}
\][/tex]
2. Calculate the Mass of One Cracker:
- We are given that the mass of 27 crackers is 24 grams.
- To find the mass of one cracker, we divide the total mass of the 27 crackers by the number of crackers:
[tex]\[
\text{Mass of One Cracker} = \frac{\text{Mass of 27 Crackers}}{27}
\][/tex]
[tex]\[
\text{Mass of One Cracker} = \frac{24 \text{ grams}}{27} \approx 0.8889 \text{ grams}
\][/tex]
3. Estimate the Number of Crackers in the Box:
- Now that we know the total mass of the crackers (596 grams) and the mass of one individual cracker (approximately 0.8889 grams), we can estimate the number of crackers in the box.
- The number of crackers is given by dividing the total mass of the crackers by the mass of one cracker:
[tex]\[
\text{Number of Crackers} = \frac{\text{Mass of Crackers}}{\text{Mass of One Cracker}}
\][/tex]
[tex]\[
\text{Number of Crackers} = \frac{596 \text{ grams}}{0.8889 \text{ grams}}
\][/tex]
[tex]\[
\text{Number of Crackers} \approx 670.5
\][/tex]
Therefore, the estimated number of crackers in the box is approximately 670.5 crackers.
