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. (

Part B: How many liters of lemon juice are present in the bottle? Show your work.

Answer 1

PART A: The answer is: x = 0.6x + 1

Let x be the total number of liquid in the bottle. l stands for lemon juice, and w stands for the water.
So, x = l + w
We know that in the bottle there is 1 liter of water, thus:
w = 1L
Further, lemon juice is 60% of the total liquid.
l = 60% · x = 60/100 · x = 0.6x

Now, let's just change this in the equation:
x = l + w
x = 0.6x +1


PART B: The answer is 1.5 L.

Let's use the equation from the part A to calculate the total amount of liquid:
x = 0.6x + 1
x - 0.6x = 1
0.4x = 1
⇒ x = 1 ÷ 0.4 = 2.5 L

Since l = 0.6x, then:
l = 0.6 · 2.5 = 1.5 L

Let's just check the answer:
x = l + w
2.5 L = 1.5 L + 1 L
2.5 L = 2.5 L