Question

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

Answer 1

part A:
Let 
t =  total the liquid in the bottle including lemon juice and water
so t =  lemon juice + water ( w = water, l = lemon juice) so t = l + w
but the bottle has 1 liter of water. and 60% lemon juice
contains 60% lemon juice = 0.6, so l = 0.6t and w(water ) = 1 liter
t = l + w
substitute l = 0.6t and w = 1 into t = l + w
now you have equation
t = 0.6t + 1

part B:
from part A, you have equation t = 0.6t +1
solve for t
 t = 0.6t +1
subtract 0.6t on both sides
t - 0.6t = 0.6t - 0.6t + 1
simplify
0.4t = 1
divide both sides by 0.4
0.4t/0.4 = 1/ 0.4
simplify
t = 2.5

2.5 liters is total including lemon juice and water
2.5 - 1(1 liter of water) = 1.5 1 liter of lemon juice

Answer 2

100%- 60%= 40%
So, we know water takes up 40% of the volume of Bruce's bottle and that the total volume of water is = 1 L. This means our total bottle volume can be found:
1Liter= $\frac{40}{100}$ v
1Liter= 0.4v
1/0.4=v
v=2.5 Liters total in Bruce's Bottle

Part A: Equation with one variable to solve for lemon juice volume.
Now that we know the total volume of Bruce's bottle, we can set the percentage of Lemon juice = (to the volume of lemon juice divided by the total volume of the bottle)* 100

Equation:
60=(j/2.5)*100

The variable used in my equation was "j" to represent the volume of lemon juice in Bruce' bottle (in Liters).


Part B: How many Liters of juice are present in the bottle? show your work.

Let's use our equation from part "A" to solve for the value of "j":
60=(j/2.5)*100
first divide each side by 100
60/100=((j/2.5)*100)/100
0.6=j/2.5
Next, to get "j" on it's own multiply both sides of the eq. by 2.5
0.6*2.5=(j/2.5)*2.5
j= 1.5 Liters