Final answer:
Chef Katrina used 3 cups of pecans and 9 cups of peanuts for her Merry Munch Mix, totaling $35.22 based on the given prices of $4.99 per cup of pecans and $2.25 per cup of peanuts.
Step-by-step explanation:
Calculating the Quantities of Pecans and Peanuts in the Merry Munch Mix
Chef Katrina uses a ratio of 1 cup of pecans to 3 cups of peanuts in her mix. We are given the cost per cup of pecans as $4.99 and the cost per cup of peanuts as $2.25. The total cost of nuts in the mix is $35.22.
To solve this, let's denote the number of cups of pecans used as p and the number of cups of peanuts as 3p (since there are three times as many peanuts as pecans). The total cost for pecans would be p times $4.99 and for peanuts 3p times $2.25.
Our equation based on the total cost is:
4.99p + 2.25(3p) = 35.22
4.99p + 6.75p = 35.22
11.74p = 35.22
Dividing both sides by 11.74 to solve for p:
p = 35.22 / 11.74
p = 3 cups of pecans
As there are three times more peanuts than pecans:
3p = 3 * 3 = 9 cups of peanuts
Therefore, Chef Katrina used 3 cups of pecans and 9 cups of peanuts in her Merry Munch Mix.