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?

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. So the 60% of lemon juice is equivalent to x liters of lemon juice.
PART A:
\[\frac{ 0.6 }{ 0.4 }=x\]


PART B: cross multiply: 0.6(1) = 0.4(x). This gives us 0.6 = 0.4x. Then we divide both sides by 0.4: 0.6/0.4 = x. Then we solve 0.6/0.4: 0.6/0.4 = 1.5. So x = 1.5. Bruce's bottle has 1.5 liters of lemon juice.

Answer 2

Part A.
Let x = the total amount of liquid in the bottle.
x is part water and part lemon juice.
60% of x, or 0.6x is lemon juice.
40% of x, or 0.4x is water. 0.4x is also 1 liter.

x = 0.6x + 0.4x
x = 0.6x + 1

If you solve this equation for x, you will get x, the total volume of liquid in the bottle.

Part B.
Let's solve the above equation.
x = 0.6x + 1
x - 0.6x = 1
0.4x = 1
x = 2.5
The total volume of liquid in the bottle is 2.5 liters.
1 liter is water, so 2.5 liters - 1 liter = 1.5 liter of lemon juice.