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
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.