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Answer :
One scoop of Cherry ice cream contains 13 grams of fat, and one scoop of Mint Chocolate Chunk contains 17 grams of fat based on the given information about Monica and Tara's ice cream sundaes.
Let's represent the grams of fat in each scoop of Cherry ice cream as "C" and the grams of fat in each scoop of Mint Chocolate Chunk as "M."
According to the given information:
For Monica:
2 scoops of Cherry ice cream = 2C grams of fat
1 scoop of Mint Chocolate Chunk = 1M grams of fat
Total fat = 43 grams
So, the equation for Monica's sundae is:
2C + 1M = 43
For Tara:
3 scoops of Cherry ice cream = 3C grams of fat
2 scoops of Mint Chocolate Chunk = 2M grams of fat
Total fat = 73 grams
So, the equation for Tara's sundae is:
3C + 2M = 73
Now we have a system of two equations with two unknowns:
2C + 1M = 43
3C + 2M = 73
Let's solve this system to find the values of C and M.
First, we can rearrange the first equation to solve for M:
M = 43 - 2C
Substitute this expression for M into the second equation:
3C + 2(43 - 2C) = 73
Simplify and solve for C:
3C + 86 - 4C = 73
-C = -13
C = 13
Now that we have the value of C, substitute it back into the expression for M:
M = 43 - 2(13)
M = 43 - 26
M = 17
Therefore, 1 scoop of Cherry ice cream contains 13 grams of fat, and 1 scoop of Mint Chocolate Chunk contains 17 grams of fat.
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