Mike's Mountain Shop prepares 3 types of trail mix: Hiker's Mix, Biker's Mix, and Mike's Special Mix. One package of Hiker's Mix uses 60 grams of raisins, 20 grams of peanuts, and 10 grams of chocolate chips. One package of Biker's Mix uses 40 grams of raisins, 40 grams of peanuts, and 20 grams of chocolate chips. One package of Mike's Special Mix uses 30 grams of raisins, 30 grams of peanuts, and 30 grams of chocolate chips. Mike has 18,000 grams of raisins, 14,000 grams of peanuts, and 7,000 grams of chocolate chips. How many packages of each type of trail mix should Mike produce to use all the raisins, peanuts, and chocolate chips?

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Mike's Mountain Shop prepares 3 types of trail mix: Hiker's Mix, Biker's Mix, and Mike's Special Mix.

One package of Hiker's Mix uses 60 grams of raisins, 20 grams of peanuts, and 10 grams of chocolate chips. One package of Biker's Mix uses 40 grams of raisins, 40 grams of peanuts, and 20 grams of chocolate chips. One package of Mike's Special Mix uses 30 grams of raisins, 30 grams of peanuts, and 30 grams of chocolate chips.

Mike has 18,000 grams of raisins, 14,000 grams of peanuts, and 7,000 grams of chocolate chips.

Let the number of packages of Hiker's Mix, Biker's Mix and Mike Special Mix to be produced to use all the ingredients be A, B and C. This gives:

60A + 40B + 30C = 18000

20A + 40B + 30C = 14000

10A + 20B + 30C = 7000

Solving the three equations gives A = 100 and B = 300

**The shop should produce 100 packages of Hiker's Mix and 300 packages of Biker's Mix to use all the ingredients.**

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