Question

A snack company makes three batches of a nut mix using the recipe shown. Each batch contains a different total amount of mix.

Answer 1

Answer:

Batch 1:  3 cups cashews; Batch 2:  1/3 cup pistachios; Batch 3:  4/3 cups almonds and 2 cups cashews

Step-by-step explanation:

Let x represent the total amount of mix.

For Batch 1, we know that the amount of pistachios is 1/6 of the total and that is 1 cup; this gives us

1/6x = 1

Multiply both sides by 6:

1/6x(6) = 1(6)

x = 6

There are 6 cups total.  1/2 of the mix is cashews; this means 1/2(6) = 3 cups is cashews.

For Batch 2, we know that the amount of almonds is 1/3 of the total and that is 2/3 of a cup; this gives us

1/3x = 2/3

Multiply both sides by 3:

1/3x(3) = 2/3(3)

x = 6/3 = 2

There are 2 cups of mix total.

1/6 of the mix is pistachios; this gives us 1/6(2) = 2/6 = 1/3 cup pistachios.

For Batch 3, we know that the amount of pistachios is 1/6 of the total mix and that is 4/6 of a cup; this means

1/6x = 4/6

Multiply both sides by 6:

1/6x(6) = 4/6(6)

x = 24/6 = 4

There are 4 cups of mix total.

1/3 of the mix is almonds; this gives us 1/3(4) = 4/3 cups almonds.  

1/2 of the mix is cashews; this gives us 1/2(4) = 2 cups cashews.

Answer 2

Convert all the nuts into sixths so p=1/6, a=2,6 and c= 3/6 and then it is simple from there. for batch 1 c would be 3 cups for batch 2 p = 1/3 and for batch 3 a,=4/3 and c=2 after simplifying