Question

Tom is making a punch that contains 80% cranberry juice and the rest ginger ale. The punch has 2 liters of ginger ale. Part A: Write an equation using one variable that can be used to find the total number of liters of cranberry juice and ginger ale in the punch. Define the variable used in the equation and solve the equation. Hint: 0.8x represents the number of liters of cranberry juice in the punch. (5 points) Part B: How many liters of cranberry juice are present in the punch? Show your work.

Answer 1

There are 8 liters of cranberry juice in the punch

Explanation:

Part A

We know that of the punch, 80% is cranberry juice.

Let's call Z the amount of cranberry juice and Y is the amount of ginger ale.

Let's call X the amount of Ponche

The amount of punch is equal to the amount of cranberry juice plus the amount of ginger ale

`X = Z + Y` (i)

Then we know that:

`Z = 0.8X` (ii)

We also know that:

`Y = 2` liters (iii)

Part B.

Now we can solve the equation:

Replace (ii) and (iii) in (i)

`X = 0.8X + 2`

`X - 0.8X = 2`

`X(1-0.8) = 2`

`X = (2)/(1-0.8)`

X = 10 liters.

Now we substitute X = 10 in equation (ii) and find the amount of Cranberry juice.

`Z = 0.8(10)`

Z = 8 liters.

There are 8 liters of cranberry juice in the punch