1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
VikaD [51]
3 years ago
11

A boy thinks he has discovered a way to drink extra orange juice without alerting his parents. For every cup of orange juice he

takes from a container of orange juice, he pours one cup of water back into the container. If he completes this process three times on the same container of juice, the resulting mixture will be exactly 50% water and 50% juice. How many cups of orange juice were originally in the container. (P.S ITS NOT 6)​
Mathematics
1 answer:
mina [271]3 years ago
6 0

Answer:

<em>x=4.8473 cups</em>

Step-by-step explanation:

<u>Concentration of Liquids </u>

It measures the amount of substance present in a mixture, often expressed as %. If there is an volume x of a substance in a total volume mix of y, the concentration is given by

\displaystyle C=\frac{x}{y}

It we take a sample of that mixture, we must consider that we are getting only the substance, but all the mixture (assumed it has been uniformly mixed). For example, if we take a glass of liquid from a 80% mixture of juice, the glass will also have a 80% of juice.

Let's solve the problem sequentially. At first, let's assume all the container is full of x cups of juice. Its concentration is 100%. Now let's take 1 cup of pure juice and replace it by 1 cup of pure water. The new amount of juice in the container is

x-1 cups of juice.

The new concentration is

\displaystyle \frac{x-1}{x}

The boy takes a second cup of liquid, but this time it's not pure juice, it has a mixture of juice and water with a concentration computed above. Now the amount of juice is

\displaystyle x-1-\frac{x-1}{x} cups of juice.

Simplifying, the cups of juice are

\displaystyle \frac{\left (x-1\right)^2}{x}

The new concentration is

\displaystyle \frac{\left (x-1\right)^2}{x^2}

For the third time, we now have

\displaystyle \frac{\left (x-1\right)^2}{x}-\frac{\left (x-1\right)^2}{x^2} cups of juice.

Simplifying, the final amount of juice is

\displaystyle \frac{\left (x-1\right)^3}{x^2}

And the final concentration is

\displaystyle \frac{\left (x-1\right)^3}{x^3}

According to the conditions of the question, this must be equal to 50% (0.5)

\displaystyle \frac{\left (x-1\right)^3}{x^3}=0.5

Taking cubic roots

\displaystyle \sqrt[3]{\frac{\left (x-1\right)^3}{x^3}}=\sqrt[3]{0.5}

\displaystyle \frac{\left (x-1\right)}{x}=\sqrt[3]{0.5}

Operating and joining like terms

\displaystyle x-\sqrt[3]{0.5}\ x=1

Solving for x

\displaystyle x=\frac{1}{1-\sqrt[3]{0.5}}

x=4.8473\ cups

Let's test our result

Final concentration:

\displaystyle \frac{\left (4.8473-1\right)^3}{4.8473^3}=0.5

You might be interested in
PLZ HELP WILL GIVE 30 POINTS AND MARK BRAINLIEST IF ANSWER ARE CORRECT. Thank you! :)
sveticcg [70]

Answer:

3) 2, 3, 4, 5

4) $10

5) B

3 0
3 years ago
Find the balance in the account after the given period. ​$2000 principal earning 6​% compounded​ annually, for 8 years. The bala
Harman [31]
Do 2000 divided by 8 than divided that by 6%
8 0
3 years ago
Read 2 more answers
27 - (2 + 3) - 10 ÷ 2
svetlana [45]

Answer:

27_5_10/2

27_5_5

22_5

17

6 0
3 years ago
Read 2 more answers
I NEED HELP ASAP PLEASE! ​
Brilliant_brown [7]

Answer:

AB = 2

Step-by-step explanation:

Using the secant- secant theorem, that is

PA × PB = PD × PC , substitute values

10(10 + AB) = 8(8 + 7)

100 + 10AB = 8 × 15 = 120 ( subtract 100 from both sides )

10AB = 20 ( divide both sides by 10 )

AB = 2

8 0
2 years ago
Select the correct answer. Which statement describes ? A. It is an irrational number. B. It is a rational number that has a repe
Nastasia [14]

Answer:

the answer is c okay g;)

Step-by-step explanation:

hope this helps

7 0
2 years ago
Other questions:
  • Suppose a bag contains 7 blue chips and 3 gold chips. What is the probability of randomly choosing a blue chip not replacing it,
    7·2 answers
  • WILL GIVE 100 POINTS
    10·1 answer
  • What is the value of xy over z if x =-2 y=-3 and z=4
    14·2 answers
  • Can someone please help me with this question!!
    14·1 answer
  • This is for the little kids what is the answer for 200-500​
    10·1 answer
  • To qualify for the postcard rate for postage, a postcard must be less than 4 1/4 inches high. Elayne has a postcard that is 4 7/
    5·2 answers
  • Each year for 3 years, the time it takes you to run a mile decreases by 10 seconds. Find the total change time
    14·1 answer
  • If 3 people go to lunch and the bill was $30 and they all give $10 and the waitress comes back with the waitress comes back and
    14·1 answer
  • Se realizó una encuesta a 10 niños sobre su preferencia en el sabor del pastel. Fresa 20% chocolate 50% y vainilla 30%. Cuál es
    12·1 answer
  • Help me please idk how to do this
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!