Answer:
4 batches
Step-by-step explanation:
Let
x -----> the number of cups of apples
y -----> the number of cups of mangoes
z -----> the number of cups of Blueberries
w -----> the number of cups of Blackberries
we know that
x/y=3/1 -----> equation A
x/z=3/2 ----> equation B
x/w=3/1 ----> equation C
x+w=16 ----> equation D
Solve the system of equations C and D
x=3w ----> equation C
x+w=16 ----> equation D
Substitute equation C in equation d and solve for w
3w+w=16
4w=16
w=4 cups of Blackberries
Remember that
For 1 batch of the recipe are used 1 cup of Blackberries
so
For 4 cups of Blackberries
The number of batches are
(1)*4=4 batches