Trent needs to produce 2000 milliliters of 45% alcohol solution. At his disposal he has 60% alcohol solution and 40% alcohol solution. How much of each does he need in order to produce his desired solution?

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 millilitre alcohol.

x millilitre solution contains millilitre alcohol.

                                            millilitre alcohol.

Similarly for 60% alcohol solution,

100 millilitre solution contains 60 millilitre alcohol.

1    millilitre solution contains millilitre alcohol.

x millilitre solution contains millilitre alcohol.

                                            millilitre alcohol.

Again for 45% alcohol solution,

100 millilitre solution contains 45 millilitre alcohol.

1    millilitre solution contains millilitre alcohol.

x millilitre solution contains millilitre alcohol.

                                            millilitre alcohol.

According to the problem,

⇒40x+120000-60x=900×100

⇒-20x=90000-120000

⇒20x = 30000

⇒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.

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