Certainly! Let's solve this step by step.
1. Determine the weight and calories of a single piece of cheese:
- Each piece of cheese weighs [tex]\( \frac{3}{2} \)[/tex] ounces.
- Each piece supplies 315 calories.
2. Calculate the number of calories per ounce:
- If [tex]\( \frac{3}{2} \)[/tex] ounces supply 315 calories, we can find the calories per ounce by dividing the total calories by the weight in ounces.
- [tex]\[
\text{Calories per ounce} = \frac{315 \text{ calories}}{\frac{3}{2} \text{ ounces}}
\][/tex]
3. Simplify the division:
- Dividing by [tex]\( \frac{3}{2} \)[/tex] is the same as multiplying by [tex]\( \frac{2}{3} \)[/tex]:
- [tex]\[
\text{Calories per ounce} = 315 \times \frac{2}{3} = 210 \text{ calories per ounce}
\][/tex]
4. Calculate the total calories for 102 ounces of cheese:
- Now that we know there are 210 calories per ounce, we can determine the total number of calories for 102 ounces:
- [tex]\[
\text{Total calories} = 210 \text{ calories per ounce} \times 102 \text{ ounces}
\][/tex]
5. Multiply to find the total calories:
- [tex]\[
\text{Total calories} = 210 \times 102 = 21420 \text{ calories}
\][/tex]
Therefore, 102 ounces of cheese supply a total of 21,420 calories.
