Answer:
10 liters of solution should be drained off and replaced with water.
Step-by-step explanation:
- Let [tex]x[/tex] be the amount in liters replaced with distilled water
As forty liters of a 60% salt solution are being reduced to a 45% solution, and we have to determine the amount in liters that must be drained and replaced with distilled water so that the resulting solution will contain only 45% salt solution.
So, the equation becomes
[tex]0.60(40-x) = 0.45(40)[/tex]
[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a[/tex]
[tex]0.6\left(40-x\right)=0.45\cdot \:40[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:0.45\cdot \:40=18[/tex]
[tex]0.6\left(40-x\right)=18[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}10[/tex]
[tex]0.6\left(40-x\right)\cdot \:10=18\cdot \:10[/tex]
[tex]\mathrm{Refine}[/tex]
[tex]6\left(40-x\right)=180[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}6[/tex]
[tex]\frac{6\left(40-x\right)}{6}=\frac{180}{6}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]40-x=30[/tex]
[tex]\mathrm{Subtract\:}40\mathrm{\:from\:both\:sides}[/tex]
[tex]40-x-40=30-40[/tex]
[tex]-x=-10[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-1[/tex]
[tex]\frac{-x}{-1}=\frac{-10}{-1}[/tex]
[tex]x=10[/tex]
Therefore, 10 liters of solution should be drained off and replaced with water.
Keywords: word problem
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