MATHEMATICS MIDDLE SCHOOL

Yasmine bought 6 gallons of apple juice. After filling up 4 bottles of the same size with apple juice, she had 0.3 gallon of apple juice left.

Answers

Answer 1

Answer:

1.425 gallons/bottle.

Further explanation

Given:

Yasmine bought 6 gallons of apple juice.
After filling up 4 bottles of the same juice, she had 0.3 gallons of apple juice left.

Question:

What is the amount of apple juice in each container (or bottle)?

The Process:

Let the amount of apple juice in each bottle as X.

The two steps for obtaining X are as follows:

Step-1: the total amount of apple juice is the initial gallon amount subtracted by the remaining gallon amount.

$\boxed{ \ 6 \ gallons - 0.3 \ gallons = 5.7 \ gallons \ }$

Step-2: the total amount of apple juice divided by the number of bottles is the amount of apple juice in each bottle.

$\boxed{ \ X = 5.7 \ gallons / 4 \ bottles = \boxed{ \ 1.425 \ gallons/bottle \ } \ }$

Let's also consider the following quick steps.

Quick steps:

$\boxed{ \ X = ((6 - 0.3) \ gallons)/(4 \ bottles) = \boxed{ \ 1.425 \ gallons/bottle \ } \ }$

Therefore, the amount of apple juice in each container (or bottle) is 1.425 gallons.

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Keyword: Yasmine bought 6 gallons of apple juice, after filling up 4 bottles, she had 0.3 gallons, what's the amount, in each bottle, subtracted by, divide, container

Answer 2

Answer:

The size of each bottle that is filled by apple juice is $\boxed{\bf 1.425}$ .

Further explanation:

Given:

Yasmine bought $6$ gallons of apple juice.

She filled up $4$ bottles of same size.

She had $0.3$ gallon of apple juice left.

Calculation:

Consider the size of each bottle is $x$ gallons.

Total size of each bottle is $4x$ gallons.

Total amount of apple juice used in these $4$ gallons can be obtained by subtracting total amount of apple juice to remaining apple juice.

$\boxed{6-0.3=5.7}$

Therefore, total size of the $4$ bottles is $5.7\text{ gallon}$ .

Write the equation for the total size of the bottles.

$\boxed{4x=5.7}$

Now find the value of $x$ which gives the size of the bottles.

$\begin{aligned}4x&=5.7\nx&=(5.7)/(4)\nx&=1.425\end{aligned}$

Therefore, the size of each bottle that is filled by apple juice is $\boxed{\bf 1.425}$ .

Simple method:

First find the total size of bottle and then divide by $4$ .

The total size of each bottle can be obtained as follows:

$6-0.3=5.7$

The size of each bottle can be obtained as follows:

$(5.7)/(4)=1.425$

The size of each bottle that is filled by apple juice is $\boxed{\bf 1.425}$ .

Learn more:

1. Learn more about algebraic expression brainly.com/question/1600376

2. Learn more about average brainly.com/question/3959122

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Algebraic expression

Keywords: Yasmine, apple juice, juice, 6 gallons, 0.3 gallons, filled, equally, bottles, juice, poured,1.425, liters, size, amount, equation, total size.

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Answer:

In geometry, a solid may exist in three-dimensional space is a TRUE statement.

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The answer to letter A is 16. The range is the difference between the greatest and smallest number

A bag holds 6 tiles: 2 lettered and 4 numbered. Without looking, you choose a tile. What is the probability of drawing a number?

Answers

The bag contains 6 tiles: 2 lettered and 4 numbered. The probability of drawing a number without looking is 2/3.

Probability is the ratio of the number of favorable outcomes and a total number of outcomes. it deals with finding out the likelihood of the occurrence of an event.

Given that,

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The task is to choose a tile from the bag without looking.

The bag contains a total of 6 tiles: 2 lettered and 4 numbered.

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The probability of drawing a number can be calculated by dividing the number of numbered tiles by the total number of tiles.

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There are 3 consecutive integers that add up to 9 which integers are they?

Answers

Answer:

The integers are 2,3,4

Step-by-step explanation:

Let one integer be = $x$

Since, the integers are consecutive, so they will increase by one.

So, 2nd integer will be = $x+1$

3rd integer will be = $x+1+1=x+2$

It is given that the 3 integers add up to 9.

So, we have the sum equation as:

$x+x+1+x+2=9$

Solving for $x$

Combining like terms.

$3x+3=9$

Subtracting both sides by 3.

$3x+3-3=9-3$

$3x=6$

Dividing both sides by 3.

$(3x)/(3)=(6)/(3)$

$x=2$

∴ 1st integer = $2$

2nd integer = $2+1 = 3$

3rd integer = $2+2 = 4$

The sum of 5 consecutive odd integers is 2,555. What is the sum of the first, third, and last integer?

Answers

Answer:

The sum of the first, third, and last integer is 1533.

Step-by-step explanation:

Step 1: You need to create a equation first:

n + n + 2 + n + 4 + n + 6 + n + 8 = 2555

How did I make the equation?

If n is odd number, n + 2 must be the consecutive odd number

5 , 5 + 2 , 5 + 4 , 5 + 6 , 5 + 8

5, 7, 9, 11, 13 ALL CONSECUTIVE ODD NUMBERS

Step 2: Simplifying the equation

n + n + 2 + n + 4 + n + 6 + n + 8 = 2555

5n + 20 = 2555

Step 3: Solving the equation, with explanation

5n + 20 = 2555 Subtract 20 on both sides

5n = 2535 Isolate the variable by dividing 5 on both sides

n = 507

Step 4: Plug in the value

n + n + 2 + n + 4 + n + 6 + n + 8

507, 507 + 2 , 507 + 4 , 507 + 6 , 507 + 8

507, 509, 511, 513, 515

Step 5: Solve the sum of the first, third, and last integer

507 + 511 + 515 = 1533

Step 6: THE ANSWER

1533

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which two numbers multiply to give you 100 and add to give you 10

Answers

The correct answer is:

There are no real numbers that fit these criteria.

Explanation:

Let x and y represent the two numbers we are looking for.

x*y = 100
x+y = 10

Solving for y,
x+y-x = 10-x
y = 10-x

Substituting this into our first equation, we have:
x(10-x) = 100

Using the distributive property,
x*10 - x*x = 100
10x - x² = 100

Writing this in standard form, we need to subtract 100 from each side:
10x - x² - 100 = 100 - 100
10x - x² - 100 = 0

In standard form, this is
-x²+10x-100 = 0.

This is in the form ax²+bx+c; in our equation, a = -1, b = 10 and c = -100.

We will use the quadratic formula for this:

$x=(-b \pm √(b^2-4ac))/(2a) \n \n=(-10\pm √(10^2-4(-1)(-100)))/(2(-1)) \n \n=(-10\pm √(100-400))/(-2) \n \n=(-10\pm √(-300))/(-2)$

There is no real square root of -300, so there are no real number solutions to this.

which two numbers multiply to give you 100 and add to give you 10:
x*y = 100
x+y = 10

x = 10 - y
x(10-x) = 100
10x - x^2 = 100

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