Answer :
Answer:
Therefore Trent needs 1500 millilitre of 40% alcohol solution and 500 millilitre of 60% alcohol solution in order to produce 2000 millilitre of 45% alcohol solution.
Explanation:
Given, Trent needs to produce 2000 millilitres of 45% alcohol solution.
Let he need x millilitre of alcohol of 40% alcohol solution.
Since total amount of alcohol is 2000 millilitres.
Then he takes (2000-x) millilitre of alcohol of 60% alcohol solution.
40 % alcohol solution means 40 units of alcohol present in 100 unit solution.
Implies that,
100 millilitre solution contains 40 millilitre alcohol.
1 millilitre solution contains [tex]\frac{40}{100}[/tex] millilitre alcohol.
x millilitre solution contains [tex]\frac{40\times x}{100}[/tex] millilitre alcohol.
[tex]=\frac{40 x}{100}[/tex] millilitre alcohol.
Similarly for 60% alcohol solution,
100 millilitre solution contains 60 millilitre alcohol.
1 millilitre solution contains [tex]\frac{60}{100}[/tex] millilitre alcohol.
x millilitre solution contains [tex]\frac{60\times(2000- x)}{100}[/tex] millilitre alcohol.
[tex]=\frac{60(2000-x)}{100}[/tex] millilitre alcohol.
Again for 45% alcohol solution,
100 millilitre solution contains 45 millilitre alcohol.
1 millilitre solution contains [tex]\frac{45}{100}[/tex] millilitre alcohol.
x millilitre solution contains [tex]\frac{45\times2000}{100}[/tex] millilitre alcohol.
[tex]=900[/tex] millilitre alcohol.
According to the problem,
[tex]\frac{40x}{100} +\frac{60(2000-x)}{100} =900[/tex]
⇒40x+120000-60x=900×100
⇒-20x=90000-120000
⇒20x = 30000
[tex]\Rightarrow x=\frac{30000}{20}[/tex]
⇒x=1500
Therefore Trent needs 1500 millilitre of 40% alcohol solution and (2000-1500)millilitre =500 millilitre of 60% alcohol solution in order to produce 2000 millilitre of 45% alcohol solution.