A trail mix recipe requires 5 cups of mixed nuts, 1 cup of raisins, 2 cups of chocolate chips, and 3 cup of pretzels for one batch. How much of each ingredient would you need for 2 batches, 3 batches, 4 batches, and 5 batches of trail mix?

Step-by-step explanation:

Mixed Nuts = 5 cups

Raisins = 1 cup

Chocolate chips = 2 cups

pretzels = 3 cups

Ingredients for 2 batches

Multiply all ingredients by 2

Mixed Nuts = 5 cups × 2

Raisins = 1 cup × 2

Chocolate chips = 2 cups × 2

pretzels = 3 cup × 2

Mixed Nuts = 10 cups

Raisins = 2 cups

Chocolate chips = 4 cups

pretzels = 6 cups

Ingredients for 3 batches

Multiply all ingredients by 3

Mixed Nuts = 15 cups

Raisins = 3 cups

Chocolate chips = 6 cups

pretzels = 9 cups

Ingredients for 4 batches

Multiply all ingredients by 4

Mixed Nuts = 20 cups

Raisins = 4 cups

Chocolate chips = 8 cups

pretzels = 12 cups

Ingredients for 5 batches

Multiply all ingredients by 5

Mixed Nuts = 25 cups

Raisins = 5 cup s

Chocolate chips = 10 cups

pretzels = 15 cups

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)