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. 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. (5 points)

Answer 1

Given that 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:

Let the number of litres of cranberry juice be x, then the total number of liters of the punch is given by x/0.8

Thus, x + 2 = x/0.8

0.8x + 1.6 = x

0.2x = 1.6

Therefore, the equation with one variable that can be used to find the total number of liters of canbelly juice and ginger ale in the punch is: 0.2x = 1.6, where x is the number of liters of canberry juice in the punch.

Part B.

Given from part A that the number of liters of canberry juice in the punch is given by 0.2x = 1.6, where x is the number of liters of canberry juice in the punch.

Therefore, the number of liters of canberry juice in the punch is x = 1.6 / 0.2 = 8 liters of canberry juice.

Answer 2

Given that 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:

Let the number of liters of cranberry juice be represented by = x

Then the total number of liters of the punch is given by
`(x)/(0.8)`

Now we have
`x+2= (x)/(0.8)` (ginger ale is also added)

Solving this, we get

`0.8x+1.6= x`

`0.2x= 1.6`

Further solving we get x = 2

So, the required equation with one variable is :
`0.2x=1.6`

Part B.

From part A we have-

`0.2x=1.6`

We will find x now, that is liters of cranberry added.

We have x =
`(1.6)/(0.2)` = 8

Hence, there is 8 liters of cranberry juice in the punch.