Question

A snack company makes three batches of a nut mix using the recipe shown.

Answer 1

Answer:

how much of each type of nut should be used in each batch.

1/3 of the mix is almonds

1/6 is pistachios

1/2 is cashews

the first batch is

P.1cup

A.2cup

C.?

Batch 2 is

P.?

A.2/3

C.1

the Third batch is

P.4/6

A.?

C.?

The answers are 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’s represent the total amount of mix with y

Batch 1

Since the amount of pistachios is 1/6 of the total and that is 1 cup which gives us

1/6y = 1

The next step is to multiply both sides by 6:

1/6y(6) = 1(6)

y = 6

We have 6 cups total.  1/2 of the mix is cashews which mean 1/2(6) = 3 cups is cashews.

Batch 2

Since the amount of almonds is 1/3 of the total and that is 2/3 of a cup which gives us

1/3y = 2/3

The next step is to multiply both sides by 3:

1/3y(3) = 2/3(3)

y = 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.

Batch 3

Since the amount of pistachios is 1/6 of the total mix and that is 4/6 of a cup which means

1/6y = 4/6

The next step is to multiply both sides by 6:

1/6y(6) = 4/6(6)

y= 24/6 = 4

Since there are 4 cups of mix total, we have  

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

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