Question

Bruce has a bottle that contains 60% of lemon juice and the rest water. The bottle has 1 liter of water.

Part A: 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.

Answer 1

Bruce's bottle is 60% (or 0.6) lemon juice and 40% (or 0.4) water. Bruce's bottle has 1 liter of water. So the 40% of water is equivalent to 1 liter of water. We don't know how many liters of lemon juice Bruce's bottle has. For now, we'll just say it has x liters of lemon juice. So the 60% of lemon juice is equivalent to x liters of lemon juice.
PART A: We can represent this with the following equation: 0.6 lemon juice/0.4 water = x liters of lemon juice/1 liter of water. In this equation, the variable x represents the liters of lemon juice.
PART B: We need to solve for x, which is the total number of liters of lemon juice. 1). we start doing this by cross multiplying: 0.6(1) = 0.4(x). This gives us 0.6 = 0.4x. 2). Then we divide both sides by 0.4: 0.6/0.4 = x. 3). Then we solve 0.6/0.4: 0.6/0.4 = 1.5. So x = 1.5. This means that Bruce's bottle has 1.5 liters of lemon juice.

Answer 2

\[0.6x +1 = x\]
\[0.4 x = 1\]
\[x = 2.5\]