Answer :
To solve this problem, we need to determine the number of calories in 180 crackers using the given data. We have two sets of data for crackers and their corresponding calorie values. Since the relationship is proportional, we can use the provided values to determine the average calories per cracker and then find the total for 180 crackers.
Let's go through the steps:
1. Calculate the calories per cracker for each given set:
For the first batch:
[tex]\[ \frac{60 \text{ calories}}{12 \text{ crackers}} = 5 \text{ calories per cracker} \][/tex]
For the second batch:
[tex]\[ \frac{75 \text{ calories}}{15 \text{ crackers}} = 5 \text{ calories per cracker} \][/tex]
2. Calculate the average calories per cracker:
Since both ratios are equal, the average calories per cracker is:
[tex]\[ \frac{5 + 5}{2} = 5 \text{ calories per cracker} \][/tex]
3. Calculate the total number of calories for 180 crackers:
[tex]\[ \text{Total calories} = 180 \text{ crackers} \times 5 \text{ calories per cracker} = 900 \text{ calories} \][/tex]
Thus, the number of calories in 180 crackers is:
[tex]\[ \boxed{900 \text{ calories}} \][/tex]
Let's go through the steps:
1. Calculate the calories per cracker for each given set:
For the first batch:
[tex]\[ \frac{60 \text{ calories}}{12 \text{ crackers}} = 5 \text{ calories per cracker} \][/tex]
For the second batch:
[tex]\[ \frac{75 \text{ calories}}{15 \text{ crackers}} = 5 \text{ calories per cracker} \][/tex]
2. Calculate the average calories per cracker:
Since both ratios are equal, the average calories per cracker is:
[tex]\[ \frac{5 + 5}{2} = 5 \text{ calories per cracker} \][/tex]
3. Calculate the total number of calories for 180 crackers:
[tex]\[ \text{Total calories} = 180 \text{ crackers} \times 5 \text{ calories per cracker} = 900 \text{ calories} \][/tex]
Thus, the number of calories in 180 crackers is:
[tex]\[ \boxed{900 \text{ calories}} \][/tex]
