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neonofarm [45]
1 year ago
10

How many gallons each of 30% alcohol and 5% alcohol should be mixed to obtain 25gal of 25% alcohol?

Mathematics
1 answer:
lozanna [386]1 year ago
4 0

Let x be the amount of the 30% alcohol and let y be the amount of 5% alcohol.

We want the total amount to by 25 gal, then we have:

x+y=25

We also want the resulting mix to be 25% alcohol, this is 0.25 in decimal form; also we know that the first type of alcohol is 30% and the second is 5%, then we have:

\begin{gathered} 0.3x+0.05y=0.25(25) \\ 0.3x+0.05y=6.25 \end{gathered}

Hence we have the system of equations:

\begin{gathered} x+y=25 \\ 0.3x+0.05y=6.25 \end{gathered}

To solve the system we solve the first equation for y:

y=25-x

then we plug this value of y in the second equation:

\begin{gathered} 0.3x+0.05(25-x)=6.25 \\ 0.3x+1.25-0.05x=6.25 \\ 0.25x=6.25-1.25 \\ 0.25x=5 \\ x=\frac{5}{0.25} \\ x=20 \end{gathered}

Once we have the value of x we plug it in the expression we found for y:

\begin{gathered} y=25-20 \\ y=5 \end{gathered}

Therefore, the mixture will have 20 gallons of 30% alcohol and 5 gallons of 5% alcohol.

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False

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Given the original number n. Multiply the number by 9. Add 99. Divide this sum by 9. Subtract the original number, n, from the q
tangare [24]

Answer:

11

Step-by-step explanation:

Hello,

Given the original number n.

\large \boxed{n}

Multiply the number by 9.

\large \boxed{9n}

Add 99.

\large \boxed{9n+99}

Divide this sum by 9.

\large \boxed{\dfrac{9n+99}{9}=n+11}

Subtract the original number, n, from the quotient.

\large \boxed{n+11-n=11}

Thank you.

4 0
3 years ago
what is the quotient 5-x/x^2 3x-4 divided by x^2-2x-15/x^2 5x 4 in simplifed form state any restrictions on the varible
zheka24 [161]

The quotient when \frac{5-x}{x^2+3x-4} /\frac{x^2-2x - 15}{x^2+5x+4} in simplified form is \frac{-(x+1)}{(x-1)(x+3)}

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that equation:

\frac{5-x}{x^2+3x-4} /\frac{x^2-2x - 15}{x^2+5x+4}

=\frac{5-x}{(x+4)(x-1)} /\frac{(x-5)(x+3)}{(x+4)(x+1)} \\\\=\frac{5-x}{(x+4)(x-1)} * \frac{(x+4)(x+1)}{(x-5)(x+3)}\\\\\frac{-(x-5)}{(x+4)(x-1)} * \frac{(x+4)(x+1)}{(x-5)(x+3)}\\\\=\frac{-(x+1)}{(x-1)(x+3)}

The quotient when \frac{5-x}{x^2+3x-4} /\frac{x^2-2x - 15}{x^2+5x+4} in simplified form is \frac{-(x+1)}{(x-1)(x+3)}

Find out more on equation at: brainly.com/question/2972832

#SPJ1

8 0
2 years ago
Jade buys a blouse and a skirt for 3/6 of their original price. Jade pays a total of $31 for the two items. If the original pric
Damm [24]

Answer:

3/4 times 18= 13.5

31.5-13.5=18  

It cost 18 dollars for the skirt with a discount.

It cost 13.5 for the blouse as opposed to the original price of 18 dollars.

18(skirt)+13.5(blouse)=31.5

If you set up a proportion to find the original price of the skirt you will get the answer.  

18/x=75/100

75x=18 times 100

75x=1800

75x/75=1800/75

x=24  

The original price of the skirt is 24 dollars.

Step-by-step explanation:

4 0
3 years ago
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