I have two bags of marbles, each of which contains some red marbles and some blue marbles (and no marbles of any other color). The ratio of red marbles to blue marbles in the first bag is $3:5.$ The ratio of red marbles to blue marbles in the second bag is $3:2.$ When the two bags of marbles are mixed together, the ratio of red marbles to blue marbles is $11:9.$ What is the ratio of the number of marbles in the first bag to the number of marbles in the second bag?

Answers

Answer 1
Answer is  2:7

========================================================

Explanation:

Let x and y be two positive whole numbers. They may or may not be equal.

The first bag has the ratio of red to blue as 3:5, which scales up to 3x:5x after multiplying both parts by x. We have 3x red and 5x blue.

The second bag has the ratio 3:2 which scales up to 3y:2y. This bag has 3y red and 2y blue.

We can make a handy table to keep track of all the expressions

[tex]\begin{array}{|c|c|c|}\cline{1-3}\text{ } & \text{Red} & \text{Blue}\\ \cline{1-3}\text{bag 1} & 3x & 5x\\ \cline{1-3}\text{bag 2} & 3y & 2y\\ \cline{1-3}\end{array}[/tex]

Based on that, we can then say:

The two red quantities add to R = 3x+3yThe two blue quantities add to B = 5x+2y

Effectively, I added down along each column of that table.

Divide the two expressions for R and B to lead to the fraction 11/9, which is directly from the ratio 11:9

So,

(total red)/(total blue) = 11/9

R/B = 11/9

(3x+3y)/(5x+2y) = 11/9

---------------------

Let's cross multiply and then solve for y

(3x+3y)/(5x+2y) = 11/9

9(3x+3y) = 11(5x+2y)

27x+27y = 55x+22y

27y-22y = 55x-27x

5y = 28x

y = 28x/5

y = (28/5)x

y = 5.6x

We'll keep this in mind for later.

---------------------

Now let:

F = amount of marbles in the first bagS = amount of marbles in the second bag

Recall that we had 3x red and 5x blue for the first bag. That means we have 3x+5x = 8x marbles in the first bag. Therefore, F = 8x.

Also, we had 3y red and 2y blue for the second bag.

So we have S = 3y+2y = 5y

Then we can apply further substitution to say

S = 5y

S = 5(5.6x) .... plug in y = 5.6x

S = 28x

---------------------

In short,

F = 8xS = 28x

for some positive whole number x. We don't have enough info to pin down what x is exactly; however, it doesn't really matter. This is because the x variable will cancel when dividing F over S

F/S = (8x)/(28x) = 8/28 = 2/7

The fraction 2/7 leads directly to the final answer of the ratio 2:7

In other words, the ratio 8x:28x simplifies fully to 2:7 after dividing both parts by 4x.

Answer 2

The ratio between the total marbles of the first bag and the second bag is 2:7.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x marbles in the first bag.

red marbles = 3x

blue marbles = 5x

y marbles in the second bag.

red marbles = 3y

blue marbles = 2y

Now,

Total red marbles in both bags.

3x + 3y = 11 _____(1)

3x = 11 - 3y

x = (11 - 3y) / 3

Total blue marbles in both bags.

5x + 2y = 9 ______(2)

From (1) and (2) we get,

Multiply 2 in (1).

6x + 6y = 22

6y = 22 - 6x _____(3)

Multiply 3 in (2)

15x + 6y = 27 ______(4)

Putting (3) in (4)

15x + 22 - 6x = 27

9x = 27 - 22

9x = 5

x = 5/9

Now,

x = 5/9 in (3)

6y = 22 - 6(5/9)

6y = 22 - 10/3

6y = (66 - 10)/3

y = 56/18

y = 28/9

Now,

First bag.

Red marbles = 3x = 3 x 5/9 = 5/3

Blue marbles = 5x = 5 x 5/9 = 25/9

Total marbles = 5/3 + 25/9 = (15 + 25)/9 = 40/9

Second bag.

Red marbles = 3y = 3 x 28/9 = 28/3

Blue marbles = 2y = 2 x 28/9 = 56/9

Total marbles = 28/3 + 56/9 = (84 + 56)/9 = 140/9

Now,

The ratio between the total marbles of the first bag and the second bag.

= 40 :140

= 4:14

= 2:7

Thus,

The ratio is 2:7.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2


Related Questions

A taxicab charges $3.00 per person
plus $1.25 per mile. What is the
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$28.00?

Answers

Answer:

I believe the answer would be 20 miles max for one passenger.

Step-by-step explanation:

This is because if you create an equation out of this, knowing that only one passenger will be riding, you will get:

$3.00+$1.25x=$28       ($3 added too $1.25 times the number of miles (x) which equals the total amount you have ($28)).

x being the number of miles (so we need to calculate for x)

$3 + $1.25x = $28

-subtract 3 on both sides-

$1.25x=$28-$3

$1.25x=$25

-divide by 1.25 on both sides-

x=$25/$1.25

x=20 miles

Not sure if all calculations are correct, but I hope this helps :)!

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Answers

[tex]\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\green{W}\red{E}\purple{R:-}}}[/tex]

[tex]:\implies\sf{ \frac{36}{x} = - 9} \\ \\ :\implies\sf{ \frac{36}{ 9} = -x} \\ \\ :\implies\sf{4 = -x} \\ \\ :\implies\sf{x = -4}[/tex]

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Answers

Answer:

a) 3.6 × 10²

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So time = 1.08 × 10⁸ / 3 × 10⁸

= 1.08 × 10¹¹ / 3 × 10⁸ ( converted 10⁸ km to meter )

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Time = 3.6 × 10²

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How do you use coordinates to find the area of polygons?

Answers

Answer:

By finding the product of a point's x coordinate times the next point's y coordinate, then subtracting the y coordinate of the first point times the x coordinate of the second coordinate and dividing by two, you will find the area of the polygon.

Step-by-step explanation:

By finding the product of a point's x coordinate times the next point's y coordinate, then subtracting the y coordinate of the first point times the x coordinate of the second coordinate and dividing by two, you will find the area of the polygon

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Answer: 3rd one got it right on mine

Step-by-step explanation:



If f(x) = 2x – 5, then what is the value of f(2) + f(5)

Answers

Answer:

4

Step-by-step explanation:

Melanie has 10 packets of 20 biscuits. She puts 3/10 of them on a plate to serve. How many biscuits are being served?

Answers

From the problem statement Melanie has 10 packets of 20 biscuits

60 biscuits

Solution

Let us find 3/10 of 10 packets

= 3 packets

In one packet there are 20 biscuits,

Hence in 3 packets there will be

20*3 = 60 biscuits

From the solution above Melanie served 60 biscuits in the plate

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the answer would be x<3/2

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Answers

The answer is: 344 + 732 = 1076

Answer:

1076

Step-by-step explanation:

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Answers

Answer:

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To calculate the area of a triangle, multiply the height by the width (this is also known as the 'base') then divide by 2. Find the area of a triangle where height = 5 cm and width = 8 cm. A triangle is always half the area of a rectangle with the same height and width.

Hey there!

“ What's the formula for the area of a triangle?”

The area of triangle formula is:

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Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Side note:

You can look at the question for an example of what the area of a triangle is

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Answers

Answer:

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Step-by-step explanation:

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Supplementary angles sum together to make 180

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Answer:

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Step-by-step explanation:

If x=2, y=4, m= -1, and n=3 find the value of :
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Answers

Answer:

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Step-by-step explanation:

Here we need to find

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HELP PLEASE IS IMPORTANT!
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Answers

See attachment for answer and math work.

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Answers

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final answer: 720 boys, 60%

Step-by-step explanation:

Hope it will help you...

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

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Step-by-step explanation

 I had this math question too  

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Answers

Answer:

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34.23×2.3=78.729

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B = {(2, 4), (−1, 4), (5, 4), (4, 4)}

a
Both A and B

b
Only B

c
Only A

d
Neither A nor B

Answers

Answer:

B

Step-by-step explanation:

A does not represent a function because the x-value of 3 appears twice, and by the defenition of a function, the x-value cannot appear twice for it to be considered a function. B could be a function because the x-values are not repeated.

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

I hope you can make sense of that


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Answers

Step-by-step explanation:

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Answers

Answer:  [tex]2x^3-2x^2-13x+3[/tex]

======================================================

Work Shown:

I'm assuming you meant to say [tex](x - 3)(2x^2 + 4x - 1)[/tex]

Let [tex]y = x-3[/tex]

So,

[tex](x - 3)(2x^2 + 4x - 1)\\\\y(2x^2 + 4x - 1)\\\\y2x^2 + y4x - y\\\\2x^2(y) + 4x(y) - (y)\\\\2x^2(x-3) + 4x(x-3) - (x-3)\\\\2x^3-6x^2 + 4x^2-12x - x+3\\\\2x^3-2x^2-13x+3\\\\[/tex]

The basic idea is to use the distribution rule (line 3 and line 6) and then combine like terms.

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Answers

Answer:

its 21

Step-by-step explanation:

first to solve right get brainlest

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Answers

Answer:

110

Step-by-step explanation:

Answer:
110

step-by-step explanation:
You havew 100 then add 100 then it becomes 200, you then subtract 200 and now you have 0 you then add 90 and add 20 which equalls to 110

10)
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Answers

Answer:

Step-by-step explanation:

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Work out 247 as a percentage of 380.

Answers

Answer:

65%

Step-by-step explanation:

You can use the equation " is over of " to solve this. 247/380 * ?/100. After simplifying, you get 24700/380  which equals 65%.

Brainliest would be appreaciated! :-)

I think the answer is 65%. Hope that helps.

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