Question

Bruce has a bottle that contains 60% of lemon juice and the rest water. The bottle has 1 liter of water. PARTA: Write an equation in one variable that can be used to find the total number of liters of lemon juice and water in the bottle. Define the variable used in the equation. (5 points) Part B: How many liters of lemon juice are present in the bottle? Show your work. (5 points)

Answer 1

The correct answers are:

2.5 L of liquid total and 1.5 L of lemon juice.

Step-by-step explanation:

Since the bottle contains 60% lemon juice, this means that 100-60 = 40% of the bottle is water. We know that there is 1 liter of water; this means we have the equation

0.4x = 1, where x is the total amount of liquid in the bottle.

Divide both sides by 0.4:

0.4x/0.4 = 1/0.4

x = 2.5

There are 2.5 L of liquid.

60% of the liquid is lemon juice; this gives us

0.6(2.5) = 1.5

There are 1.5 L of lemon juice.

Answer 2

Let x= the total volume of liquid the bottle can hold.
Since 40% of the liquid is water, then .4x = 1L

Then you solve for x.

0.4x=1L
0.4x/0.4 = 1L/0.4
x = 2.5 L

So we have the total volume of the bottle which is 2.5 L.

Now, let the number of liters of lemon juice be y.
y=0.6x
So the equation would be x = 0.4x + y
or simply, x = .4x + .6x

Solve for y.
y= 0.6(2.5L)
y= 1.5L

So the amount of lemon juice in the bottle is 1.5 L.