The problem begins with 18 liters of a mixture of oil and water. x liters of water are to be added to the mixture thus the final mixture will have 18 + x liters.
The equation can be written by representing the amount of oil in each step or the amount of water in each step.
If we use the percentage of oil we start with 15% of 18 liters or 0.15(18) the amount of oil in the beginning. x liters of water are being added which has 0% oil, thus the amount of oil added is 0(x). The resulting mixture has 12% oil so the amount of oil in the resulting mixture is 0.12(18 + x)
The equation is: 0.15(18) + 0x = 0.12(18 + x)
2.7 = 2.16 + 0.12x
0.54 = 0.12x
4.5 = x
If the equation is written for the amount of water in each step, we begin with 85% water of 18 liters or 0.85(18). X liters of 100% water are being added so 1.00x liters of water is being added. The result has 88% water so the amount of water is the resulting mixture is 0.88(18 + x)
The equation is: 0.85(18) + 1x = 0.88(18 + x)
15.3 + x = 15.84 + 0.88x
15.3 + 0.12x = 15.84
0.12x = 0.54
x = 4.5
Thus 4.5 liters of water should be added.
