Answer:
120 liters of the 10% solution should be mixed with 60 liters of a 25% solution to get a 15% solution.
Step-by-step explanation:
Let 'x' be the quantity of 10% solution
Given that we need determine many liters of a 10% solution should be mixed with 60 liters of a 25% solution to get a 15% solution.
As
10% of x = 0.1x
60 liters of a 25% = 60 × 0.25
Thus,
The equation becomes
[tex]0.1x+60\times \:0.25=0.15\left(x+60\right)[/tex]
Multiply both sides by 100
[tex]0.1x\times \:100+15\times \:100=0.15\left(x+60\right)\times \:100[/tex]
[tex]10x+1500=15\left(x+60\right)[/tex]
[tex]10x+1500=15x+900[/tex]
Subtract 1500 from both sides
[tex]10x+1500-1500=15x+900-1500[/tex]
Simplify
[tex]10x=15x-600[/tex]
Subtract 15x from both sides
[tex]10x-15x=15x-600-15x[/tex]
Simplify
[tex]-5x=-600[/tex]
Divide both sides by -5
[tex]\frac{-5x}{-5}=\frac{-600}{-5}[/tex]
Simplify
[tex]x=120[/tex]
Therefore,
- 120 liters of the 10% solution should be mixed with 60 liters of a 25% solution to get a 15% solution.
