Answer: 20 cups of grape juice are needed for 8 cups of peach juice.
Step-by-step explanation:
5 times 4 is 20.
We must do this step because you need 2 cups for 1 batch, and times 4 that is 8. So then we multiplied 5 times 4.
So, 20 cups of grape juice are needed for 8 cups of peach juice.
Hope this answer helps you out!

Expanding the left side gives

which gives two solutions,

and

. But if

, then

, but this number isn't real, so

is an extraneous solution. Meanwhile if

, you get

, so this solution is correct.
"Potential solutions" might refer to both possibilities, but there is only one actual (real) solution.
Answer:

Step-by-step explanation:
Let the numbers be x,y, where x>y
The geometric mean is

The Arithmetic mean is

The ratio of the geometric mean and arithmetic mean of two numbers is 3:5.

We can write the equation;

or

l
and

or

Make y the subject in equation 2

Put equation 3 in 1





When x=1, y=10-1=9
When x=9, y=10-9=1
Therefore x=9, and y=1
The ratio of the smaller number to the larger number is

The coefficient is what the bariable is multiplied by. In this case, the variable is x and it is multiplied by 4