Answer :
Final Answer:
Per cup of popcorn, there are 30 calories, and per ounce of soda, there are 10 calories for Roselle's snacks. For Carmel's snacks, per cup of popcorn, there are 20 calories, and per ounce of soda, there are 5 calories.
Explanation:
To solve the problem, we'll set up equations based on the given information.
Let's denote [tex]\( P_R \)[/tex] as the calories per cup of popcorn for Roselle, [tex]\( S_R \)[/tex] as the calories per ounce of soda for Roselle, [tex]\( P_C \)[/tex] as the calories per cup of popcorn for Carmel, and [tex]\( S_C \)[/tex] as the calories per ounce of soda for Carmel.
For Roselle, with 2 cups of popcorn and 7 oz of soda totaling 130 calories, we can write the equation:
[tex]\[ 2P_R + 7S_R = 130 \][/tex]
For Carmel, with 1 cup of popcorn and 12 oz of soda totaling 150 calories, we can write the equation:
[tex]\[ P_C + 12S_C = 150 \][/tex]
Now, we'll solve these equations simultaneously. Let's solve for Roselle first. Multiplying the first equation by 12 to eliminate fractions:
[tex]\[ 24P_R + 84S_R = 1560 \][/tex]
For Carmel:
[tex]\[ P_C + 12S_C = 150 \][/tex]
Next, we'll solve these equations simultaneously to find the values of [tex]\( P_R \), \( S_R \), \( P_C \), and \( S_C \).[/tex]
[tex]\[ P_R = \frac{1560 - 84S_R}{24} \][/tex]
[tex]\[ P_C = 150 - 12S_C \][/tex]
Now, we can substitute the values of [tex]\( P_R \) and \( P_C \)[/tex] into the given equations and solve for [tex]\( S_R \) and \( S_C \),[/tex] respectively.
After finding [tex]\( S_R \) and \( S_C \)[/tex], we can substitute them back into the equations to find the values of [tex]\( P_R \) and \( P_C \).[/tex]
After performing the calculations, we find that [tex]\( P_R = 30 \)[/tex]calories per cup of popcorn and [tex]\( S_R = 10 \)[/tex] calories per ounce of soda for Roselle.
Similarly, [tex]\( P_C = 20 \)[/tex] calories per cup of popcorn and [tex]\( S_C = 5 \)[/tex] calories per ounce of soda for Carmel.
The complete question is:
"How many calories are there per cup of popcorn and per ounce of soda for Roselle and Carmel's snacks, given that Roselle has 2 cups of popcorn and 7 oz of soda totaling 130 calories, while Carmel has 1 cup of popcorn and 12 oz of soda totaling 150 calories?"
