To determine how many calories are in 180 crackers given that the relationship between crackers and calories is proportional, we need to follow these steps:
1. Understand the Proportional Relationship:
- We know from the problem statement that there are 60 calories in 12 crackers and 75 calories in 15 crackers. This indicates a proportional relationship.
- Let's denote the number of crackers by [tex]\( x \)[/tex] and the number of calories by [tex]\( y \)[/tex].
2. Calculate Calories per Cracker:
- By calculating the calories per cracker for the given data points, we can establish the consistency of the proportionality.
[tex]\[
\text{Calories per cracker} = \frac{\text{Calories}}{\text{Crackers}}
\][/tex]
For 12 crackers:
[tex]\[
\frac{60 \text{ calories}}{12 \text{ crackers}} = 5 \text{ calories per cracker}
\][/tex]
For 15 crackers:
[tex]\[
\frac{75 \text{ calories}}{15 \text{ crackers}} = 5 \text{ calories per cracker}
\][/tex]
3. Determine the Total Calories for 180 Crackers:
- Now that we have established that there are 5 calories per cracker, we can use this ratio to find the total calories for 180 crackers.
[tex]\[
\text{Calories per cracker} \times \text{Number of crackers} = \text{Total calories}
\][/tex]
[tex]\[
5 \text{ calories per cracker} \times 180 \text{ crackers} = 900 \text{ calories}
\][/tex]
Therefore, there are 900 calories in 180 crackers.
