Kongkangidn
Answered

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How many liters of water must be added to 50 liters of 70% alcohol to produce a 50 alcohol?

Sagot :

Iucciidn

Answer:

20 liters

Step-by-step explanation:

[tex]\rm 0.7 x 50 = 0.5(50 + x)[/tex]

[tex]\rm 35 = 25 + 0.5x[/tex]

[tex]\rm 0.5x = 10[/tex]

[tex]\rm x = 20 \: liters[/tex]

Therefore, you'll need to add 20 liters of water to the 50 liters of 70% alcohol solution to get a final solution of 50% alcohol.

MrChrisidn

[tex] \underline{\underline{\large{\red{\mathcal{ ✒ GIVEN:}}}}} [/tex]

[tex]\bullet \: \: \rm{50 \: liters \: of \: 70 \%}[/tex]

[tex]\bullet \: \: \rm{Final \: solution = 50 \% \: alcohol}[/tex]

[tex] \underline{\underline{\large{\red{\mathcal{REQUIRED:}}}}} [/tex]

How many liters of water are needed to make the 50% alcohol solution?

[tex] \underline{\underline{\large{\red{\mathcal{SOLUTION:}}}}} [/tex]

First, calculate the amount of pure alcohol in the initial solution.

[tex]\tt{50 \times 0.70 = 35 \: liters}[/tex]

Let [tex]\rm{x}[/tex] be the amount of water to be added. The total volume of the new solution must be 50 + x liters and 50% alcohol. So, we can set up the following equation.

[tex]\tt{35 =( 50 + x) \times 0.50}[/tex]

Solving the equation for x:

[tex]\tt{35 = 25 + 0.50x}[/tex]

[tex]\tt{0.50x = 35 - 25}[/tex]

[tex]\tt{0.50x=10}[/tex]

[tex]\tt{x = \dfrac{10}{0.50} }[/tex]

[tex]\large{\tt{\purple{x=20 \: liters}}}[/tex]

Final Answer:

Therefore, 20 liters of water must be added to 50 liters of 70% alcohol to produce 50% alcohol solution.

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