Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

How many gallons each of
15% alcohol and
10% alcohol should be mixed to obtain 5 gal of
11% alcohol?

Gallons of

Solution

Percent

(as a decimal)

Gallons of

Pure

Alcohol

x

15%=0.15

y

10%=0.1

5

11%=

How many gallons of
15% alcohol should be in the mixture?
◻ gal

How many gallons each of $15 \%$ alcohol and $10 \%$ alcohol should be mixed to obtain $5$ gal of $11 \%$ alcohol? $\newline$ \begin{tabular}{|c|c|c|} $\newline$ \hline \begin{tabular}{c} $\newline$ Gallons of \\ $\newline$ Solution $\newline$ \end{tabular} & \begin{tabular}{c} $\newline$ Percent \\ $\newline$ (as a decimal) $\newline$ \end{tabular} & \begin{tabular}{c} $\newline$ Gallons of \\ $\newline$ Pure \\ $\newline$ Alcohol $\newline$ \end{tabular} \\ $\newline$ \hline $x$ & $15 \%=0.15$ & \\ $\newline$ \hline $y$ & $10 \%=0.1$ & \\ $\newline$ \hline $5$ & $11 \%=$ & \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ How many gallons of $15 \%$ alcohol should be in the mixture? $\square$ gal

View step-by-step help

View step-by-step help

Weighted averages: word problems

Full solution

Q. How many gallons each of

15 \%

alcohol and

10 \%

alcohol should be mixed to obtain

5

gal of

11 \%

alcohol?

\newline

\begin{tabular}{|c|c|c|}

\newline

\hline \begin{tabular}{c}

\newline

Gallons of \\

\newline

Solution

\newline

\end{tabular} & \begin{tabular}{c}

\newline

Percent \\

\newline

(as a decimal)

\newline

\end{tabular} & \begin{tabular}{c}

\newline

Gallons of \\

\newline

Pure \\

\newline

Alcohol

\newline

\end{tabular} \\

\newline

\hline

x

&

15 \%=0.15

& \\

\newline

\hline

y

&

10 \%=0.1

& \\

\newline

\hline

5

&

11 \%=

& \\

\newline

\hline

\newline

\end{tabular}

\newline

How many gallons of

15 \%

alcohol should be in the mixture?

\square

gal

Define Variables: Let $x$ be the gallons of $15\%$ alcohol and $y$ be the gallons of $10\%$ alcohol. We know that $x + y = 5$ because we want $5$ gallons of the final mixture.
Calculate Total Alcohol: We also know that the amount of pure alcohol in the $15$ \% solution is $0.15x$ and in the $10$ \% solution is $0.1y$ . The final mixture has $11$ \% alcohol, so the total pure alcohol in the final mixture is $0.11 \times 5$ .
Set Up Equation: Now we can set up the equation for the total pure alcohol: $0.15x + 0.1y = 0.11 \times 5$ .
Substitute and Simplify: Substitute $y$ with $5 - x$ (from the first equation) into the alcohol equation: $0.15x + 0.1(5 - x) = 0.55$ .
Combine Like Terms: Distribute the $0.1$ into the parentheses: $0.15x + 0.5 - 0.1x = 0.55$ .
Isolate Variable: Combine like terms: $0.05x + 0.5 = 0.55$ .
Solve for x: Subtract $0.5$ from both sides: $0.05x = 0.05$ .
Solve for x: Subtract $0.5$ from both sides: $0.05x = 0.05$ . Divide both sides by $0.05$ to solve for x: $x = \frac{0.05}{0.05}$ .

More problems from Weighted averages: word problems

Question

Eric made a scale drawing of the auditorium. The stage, which is \(35\) feet wide in real life, is \(5\) inches wide in the drawing. What is the scale of the drawing? \(1\) inch :

\_\_\_\_\_

Posted 1 month ago

Question

\newline

66

=

\_\_\_\_\_

Posted 1 month ago

Question

Wyatt, a chemist at a chemical supply company, has carefully measured out

100

gallons of a solution containing

14\%

acetone. He also has access to unlimited quantities of a

9\%

acetone solution. How many gallons of the

9\%

acetone solution must Wyatt add to the

14\%

acetone solution to create a solution that contains

10\%

\newline

Write your answer as a whole number or as a decimal rounded to the nearest tenth.

\newline

\newline

\newline

Posted 1 month ago

Question

William recently started running after school. Yesterday, he ran

4.8

41

6

seconds. Today, he ran

4.1

33

4

seconds. What was William's average speed over the two runs?

\newline

Write your answer as a whole number, a decimal, or a simplified fraction or mixed number. Do not round.

\newline

\newline

____ miles per minute

\newline

Posted 1 month ago

Question

\newline

750

=

Posted 1 month ago

Question

\newline

250

=

Posted 1 month ago

Question

An electrolyte solution has an average current density of

1\,\frac{\text{A}}{\text{dm}^2}

\newline

What is the current density of the solution in

\frac{\text{A}}{\text{m}^2}

\newline

\square

\frac{\text{A}}{\text{m}^2}

Posted 1 month ago

Question

The formula for the length of the hypotenuse in a right triangle is

\sqrt{a^{2}+b^{2}}

a

b

are the lengths of the triangle's sides (this formula is derived from the Pythagorean theorem).

\newline

From the side, a certain ramp has a right-triangular shape. Its height is

30

centimeters and its horizontal length is

3

\newline

What calculation will give us the estimated length of the ramp in meters?

\newline

1

\newline

\sqrt{\left(\frac{30^{2}}{100^{2}}\right)+3^{2}}

\newline

\sqrt{30^{2}+3^{2}\cdot 100^{2}}

\newline

\sqrt{30^{2}\cdot 100^{2}+3^{2}}

\newline

\sqrt{30^{2}+\left(\frac{3^{2}}{100^{2}}\right)}

Posted 1 month ago

Question

Roselyn is driving to visit her family, who live

150

kilometers away. Her average speed is

60

kilometers per hour. The car's tank has

20

liters of fuel at the beginning of the drive, and its fuel efficiency is

6

kilometers per liter. Fuel costs

0.60

dollars per liter.

\newline

What is the price for the amount of fuel that Roselyn will use for the entire drive?

\newline

Posted 1 month ago

Question

David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is

15 : 1

. He currently has

40

grams of the spice blend, and he can go buy more if necessary. He wants to make

10

servings, where each serving has

75

grams of rice. Overall, David spends

4.50

dollars on rice.

\newline

How many servings can David make with the current amount of spice he has?

\newline

\square

Posted 28 days ago