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.
