Question

Alice wants to make a trail mix of nuts and dried fruit. She has κ kilogram of peanuts and κ kilogram of dried cranberries. She purchases κ kilogram of almonds and 1/12 kilogram of raisins to mix with the peanuts and cranberries. After mixing the four ingredients, how many kilograms of nuts and how many kilograms of dried fruit will there be in the trail mix?

Answer 1

There would be 3κ kilograms of nuts and κ + 1/12 kilogram of dried fruit in the trail mix.

Step-by-step explanation:

To find out how many kilograms of nuts and dried fruit will be in the trail mix, we need to add up the weights of all the ingredients. Alice has κ kilogram of peanuts, κ kilogram of dried cranberries, κ kilogram of almonds, and 1/12 kilogram of raisins. The total weight of the nuts would be κ + κ + κ = 3κ kilograms. The total weight of the dried fruit would be κ + 1/12 kilogram. Hence, the trail mix comprises 3κ kilograms of nuts and κ + 1/12 kilogram of dried fruit, derived from summing the nut weights and accounting for the combination of various quantities of dried fruit components present in Alice's inventory.