To solve the problem, we need to determine how many grams of fat are in one scoop of Cherry ice cream and one scoop of Mint Chocolate Chunk ice cream. We can set up a system of equations based on the information provided:
1. Camille's sundae consists of 2 scoops of Cherry ice cream and 1 scoop of Mint Chocolate Chunk ice cream totaling 46 grams of fat.
2. Sasha's sundae consists of 3 scoops of Cherry ice cream and 2 scoops of Mint Chocolate Chunk ice cream totaling 77 grams of fat.
Let's define:
- [tex]\( C \)[/tex] as the grams of fat per scoop of Cherry ice cream
- [tex]\( M \)[/tex] as the grams of fat per scoop of Mint Chocolate Chunk ice cream
Based on the given data, we can write two equations:
1. [tex]\( 2C + M = 46 \)[/tex]
2. [tex]\( 3C + 2M = 77 \)[/tex]
To solve this system of equations, we can use the method of elimination or substitution. Let's use the elimination method:
First, let's multiply the first equation by 2 to make the coefficients of [tex]\( M \)[/tex] the same in both equations:
[tex]\[ 2(2C + M) = 2 \times 46 \][/tex]
[tex]\[ 4C + 2M = 92 \][/tex]
Now, we have the system:
1. [tex]\( 4C + 2M = 92 \)[/tex]
2. [tex]\( 3C + 2M = 77 \)[/tex]
Next, we subtract the second equation from the first:
[tex]\[ (4C + 2M) - (3C + 2M) = 92 - 77 \][/tex]
[tex]\[ 4C + 2M - 3C - 2M = 15 \][/tex]
[tex]\[ C = 15 \][/tex]
So, the number of grams of fat per scoop of Cherry ice cream is 15 grams.
Now, substitute [tex]\( C = 15 \)[/tex] back into the first equation to solve for [tex]\( M \)[/tex]:
[tex]\[ 2(15) + M = 46 \][/tex]
[tex]\[ 30 + M = 46 \][/tex]
[tex]\[ M = 46 - 30 \][/tex]
[tex]\[ M = 16 \][/tex]
So, the number of grams of fat per scoop of Mint Chocolate Chunk ice cream is 16 grams.
Therefore, the correct answer is:
- Cherry has 15 grams of fat
- Mint Chocolate Chunk has 16 grams of fat
The answer is:
a. Cherry has 15 g of fat and Mint Chocolate Chunk has 16 g of fat.
