The ratio of athletes in the two teams is 3:2. After 12 athletes move from first team to second, the ratio is 5:4. Find the number of athletes on each team originally.

Answers

Answer 1

Answers:

team one = 162team two = 108

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

Explanation:

The ratio 3:2 scales up to 3x:2x for some positive whole number x.

This tells us that the first team has 3x people and the second team has 2x people. We'll subtract 12 from the first team and add 12 to the second team to represent 12 people moving.

3x becomes 3x-122x becomes 2x+12

The new team counts 3x-12 and 2x+12 represent team 1 and team 2. Those expressions are in the new proportion 5:4.

This means....

(team 1 new count)/(team 2 new count) = 5/4

(3x-12)/(2x+12) = 5/4

4(3x-12) = 5(2x+12)

12x-48 = 10x+60

12x-10x = 60+48

2x = 108

x = 108/2

x = 54

From this, we then can say:

team 1 original count = 3x = 3*54 = 162team 2 original count = 2x = 2*54 = 108

The two subtotals add to 162+108 = 270 players overall.

If we were to subtract 12 from team 1, and add 12 to team 2, then,

team 1 new count = 162-12 = 150team 2 new count = 108+12 = 120

The ratio 150:120 then reduces to 5:4 when we divide both parts by the GCF 30. This helps confirm we have the correct answer.

Answer 2

Answer:

162 athletes108 athletes

Step-by-step explanation:

Each ratio can be expressed using two numbers that have the same sum. The sum in the first given ratio is 3+2 = 5, and in the second ratio, it is 5+4 = 9. The least common multiple of 5 and 9 is 45, so we can express both ratios so they have a sum of 45:

  3 : 2 = 3(9) : 2(9) = 27 : 18

  5 : 4 = 5(4) : 4(5) = 25 : 20

Here, we observe that the second ratio has numbers that look like 2 was moved from the numerator to the denominator. (27 -2 = 25; 18 +2 = 20) The problem statement tells us 12 athletes were moved, so multiplying the first ratio by 12/2 = 6 will tell us the numbers of players on each original team:

  first team = 27×6 = 162 athletes

  second team = 18×6 = 108 athletes


Related Questions

Can anybody help me with this question and show me how to do it step by step, ASAP?! Btw, this question is for solving systems by elimination. I really need to sleep, and I just want to get a good grade on this.

Carl bought 19 apples of 2 different varieties to make a pie. The total cost of the apples was $5.10. Granny Smith apples cost $0.25 each and Gala apples cost $0.30 each. How many of each type of apple did Carl buy?

Answers

Answer:

Step-by-step explanation:

Split 19 into 2, since Carl bought two types of apples.

19/2 = 9.5

0.25 x 9 = 2.25

0.3 x 9 = 2.7

2.25 + 2.7 = 4.95

5.10 - 4.95 = 0.15

0.3 x 8 = 2.4

2.25 + 2.4 = 4.65

5.1 - 4.65 = 0.45

Pls help i don't get this. I will give brainliest
Rick paints a circular table that has a diameter of 16. What is the area of the table?

Answers

Answer:201.06

Step-by-step explanation:

area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]

Radius of table = d/2 = 16/2 = 8

The area of the table = 8^2 x [tex]\pi[/tex] = 64[tex]\pi[/tex] = 201.06 (2.d.p)

The area of the circular table is 201.06

what is 54 x 67 ? Plz help!!!!

Answers

Answer:

3618

Step-by-step explanation:

Which measure of spread is the most appropriate for the data set represented by the graph?



A.
range
B.
quartiles
C.
interquartile range
D.
mean absolute deviation
it is not D.
E.
either range or interquartile range

Answers

your answer is B
explanation:

Answer:

B

Step-by-step explanation:

becasue the guy above is correct

10 divided by 2 pa answer po grade 3 po ako

Answers

Answer:

10 divided 2 is 5 this is correct

Step-by-step explanation:

hope it help

10 divided by 2 = 5
5x2=10
5+5=10
10-5=5

please help me ! I will give 20 points ! ( also have a great day :> )

Answers

Answer:

343

Step-by-step explanation:

7 * 7 * 7

7 * 7 = 49

49 * 7 = 343

About 6% if the golf course in the united states are in florida. in 2008 there 17,151 golf courses in the united states, about how many of them are in florida?? Please help nowwwww!

Answers

Answer:

Step-by-step explanation:

hope that help you

Answer:

1029.06

Step-by-step explanation:

You need to change 6% to a decimal

6% = .06

Then multiply .06 by 17,151

0.6 times 17,151 = 1029.06

To Check:

1029.06 out of 17,151

That's pretty much equal to 1/17

As a percentage, 1/17 is 6%

please I need help with this:) 12 points!!
Will give brainliest to the correct answer!1.

Answers

Answer:

Part A:  -1/4

Part B:  2/5

Step-by-step explanation:

Please use the pic and help me :)

Answers

16

48 * (1/3), equals 16
She wants to be 1/3 Of(multiply)

Answer:

16 feet

Step-by-step explanation:

Since Breanna's mom's garden is 48 feet in length, we can multiply that by 1/3 or divide by 3 to get the length of Breanna's garden. 48 / 3 = 16, so the answer is 16 feet.

help me plzzzzzz 5 buck

Answers

Answer:

The unit rate for the first bag is about 2.50 and for the second bag it is about 2.42. The second bag is the better bag because it has a smaller unit rate.

Step-by-step explanation:

Divide the amount of money by the weight of each bag to find the unit rate.

A i do believe

Step-by-step explanation:

An employee earns a 25% commission rate on his sales. One day, he earned $175. What was his amount of sales?
Help Please

Answers

Answer:

$700

Step-by-step explanation:

25% = 1/4

the sales would be 100% or 4/4

So if commission rate is 1/4, to find the sales we multiply this by 4:

$175*4= $700

The sales would amount to $700

Hope this helps :)

Sales amount =$700
Merry Christmas

Pls answer it i will give brainly and no links pls ty worth 29 points

Answers

I think the answer is 7. 5 miles

Answer:

7.5mph (1 d.p)

Step-by-step explanation:

First, I worked out what a third of an hour was to match the unit mph.

60 minutes / 3 = 20 mins

A third of an hour is 20minutes so two thirds of an hour is 40 minutes.

But as we know, one third as a decimal is 0.33(reccuring) so therefore two thirds as a decimal is 0.66, which we need to use.

Now, we need to remember the equation. Speed = distance / time

Place the facts we already know in place.

speed = 5miles / 0.66 (using a calculator.)

speed = 7.5mph (1 d.p)

Hope this helps and you have a good day!

HELP PLEASE!

Which diagram represents a fraction equivalent to 40%? ​

Answers

Answer:

2/5. hope this helps.

Step-by-step explanation:

2/5 has a decimal of 0.4, and the percentage is 40%.

the answer is 2/4 pick that and you’ll get it right

Hi, I need some help with the last question of the first problem and the answer to the second page.

Answers

Answer:

46.9 for the first one

Step-by-step explanation:

So sorry if i'm wrong <3

A middle school has an oval track with the dimensions shown. What is the distance around the track? use 3.14 for π. show your work.

Answers

I think the asnwear is 10859.94
I’m sorry if I’m wrong :{

The distance around the oval track would be 556.9 m which is the sum of the perimeter of the square and the circumference of the semi-circles.

What is the Circumference of a circle?

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

C = πd

where 'd' is the diameter of the circle

We have to determine the distance around the track

The required distance is equal to the sum of the perimeter of the square and the circumference of the semi-circles.

A middle school has an oval track with the dimensions shown.

Here the length of a side of the square = 78 m

And the diameter of the circle = 78 m

the distance around the track = perimeter of  square + circumference of the circle

the distance around the track = 4 × 78 + π × 78 / 2 + π × 78 / 2

the distance around the track = 4 × 78 + π × 78

the distance around the track = (4 + π) × 78

the distance around the track = (4 + 3.14) × 78

the distance around the track = 7.14 × 78

the distance around the track = 556.9 m

Therefore, the distance around the oval track would be 556.9 m.

Learn more about the Circumference of the circle here:

brainly.com/question/19794723

#SPJ5

Last two plz help!!(ty for all the help) :

14. Factor the following:
I. b2 + b - 12
j. k2 - 5k + 6

Answers

Answer:

I= (b-3) (b+4) J= (k-3) (k-2) :)

Step-by-step explanation:

Answer:

I. (B^2 + B -12) is (b-3)(b+4)

J. K^2 -5K + 6 is (k-3)(k-2)

Hope this helps

- Andrew

Can someone help me with these?

Answers

Answer:

1:100 and 1:14

Step-by-step explanation:

Answer:

It’s 1:100 and 1:14

Wish its the right Answer

i never learned fractions… plz help

Answers

Answer:

3/10 ÷ (-4/5) = 3/8 and then for the bottom one is -1 7/8 and for the one in the right is 6 2/5

The first picture will be 3/8 and second picture will be 7

Proportional relationship between x y cabbage

Answers

Answer:

10 pounds cost $4.00

Step-by-step explanation:

10 pounds cost 4.00

The Ramirez family has a circular garden with a diameter of 22 feet. They cover the garden with mulch. The cost of mulch is $1.25 per square foot. To the nearest dollar, how much will it cost to cover the garden with mulch. Show your work.

A.$380 B. $475
C. $1.520 D. 1.900

Answers

Answer:

b) $475

Step-by-step explanation:

if it has a diameter of 22 feet, that means it has a radius of 11 feet

the formula of the area of a circle is πr². so square the radius and you will get 121, multiply that by π and you get 380

Now we know the area is 380 square feet, so multiply that by $1.25 and the answer is $475

b) $475
Step-by-step explanation:
if it has a diameter of 22 feet, that means it has
a radius of 11 feet
the formula of the area of a circle is Tr?. so
square the radius and you will get 121, multiply
that by TI and you get 380
Now we know the area is 380 square feet, so
multiply that by $1.25 and the answer is $475

Wich ratio is equivalent to 14:4?
A. 21:8
B. 35:15
C. 49:14
D. 7:3

Answers

Answer:

C

Step-by-step explanation:

To calculate the left side of the ratio, our calculator multiplies the right side by 14 and then divides the product by 4. To calculate the right side of the ratio, our calculator multiplies the left side by 4 and then divides the product by 14. Answers are rounded to two decimals if necessary.

C not step to step it’s just c

Yohanna is conditioning all summer to prepare for her high school’s varsity soccer team tryouts. She is incorporating walking planks into her daily training plan. Every day, she will complete five more walking planks than the day before. Yohanna starts with four walking planks on the first day. Write an explicit formula that can be used to find the number of walking planks she completes on any given day. Use the formula to calculate the number of walking planks Yohanna will do on the 11th day?

Answers

Answer:

[tex]X+5[/tex] ; On the 11th day she will do 53 planks

Step-by-step explanation:

Day:   # of planks:

1st :    3

2nd:  8

3rd:   13

4th:   18

5th:   23

6th:   28

7th:   33

8th:   38

9th:   43

10th:  48

11th:   53

Can someone explain to me what this means, I can't quite understand it.

Answers

Answer: 214 You added up all of those and devided the mean( all 4)

PLEASE HELP FAST! DUE TODAY AND CANT HAVE A 0!

Answers

Answer:

ok so i think it is 5/9

Step-by-step explanation:

both equal 0.5 in decimal point

Answer:

The last option is correct

Step-by-step explanation:

Eg: i take  -4/9

If your answer id 4/-9 , the negative sign will always go on the top so answer will be -4/9

Thus its similar

Hope you understood

if not I will explain again !

Your welcome !

2/5 divided by 6/7 in FRACTION FORM

no links, out of context answers, or vile comments, ty

Answers

Answer:

Step-by-step explanation:

Find the reciprocal of the divisor

Reciprocal of

6/7 : 7/6

Now, multiply it with the dividend

So, 2/5 ÷ 6/7 = 2/5 × 7/6

= 2 × 7/5 × 6

= 14/30

After reducing the fraction, the answer is

7/15

Fiona is taking some time to balance her check register at the end of the month. Use the check register to answer questions for 6 and 7. Based on the transactions, what was the balance in Fiona’s account after she deposited her birthday gift on 6/4?


$780

$690

$340

$430

Answers

$690
Is the corrects answer
Hope this helps

PLZ HELP AS SOON AS POSSIBLE!!!!!!!!! WILL GIVE LIKE, 5 STARS, & BRAINLIEST; THE WHOLE SHEBANG;
Part 1
Meg is a veterinarian. She found that 5 or, 50% of the dogs she saw this week were boxers. Steve is also a veterinarian. He found that 50% out of the 2 dogs he saw this week were boxers. Does each person need to find the​ part, the​ whole, or the​ percent?
Question content area bottom
Part 1
Meg needs to find the

percent.
part.
whole.
Part 2
Steve needs to find the

percent.
part.
whole.

Answers

Answer:

Part 1: meg needs to find the whole

Part 2: steve needs to fing the part

hope this helped!

HELP DUE AT 9:00 PM!

Answers

A is 5,6 that is the answer for A gotta go but maybe someone else can help with the other ones
B is (-7,1) C is (-4,-7) and D is (9,1)

what is (0.25) x (1.4)

Answers

(0.25) x (1.4) = 0.35

Answer:

0.35

tep-by-step explanation:

24 is 0.2​% of what​ number?

Answers

Answer:

12,000

Step-by-step explanation:

Other Questions
Rewrite the following formal sentence in a more conversational style. This may require the use of more than one sentence. Make changes to both sentence structure and word choices.It ill becomes us to cast about for someone to blame, to flee unpleasant realities, orto hide the clear facts in a cloud of finger-pointingwe must take responsibility. At what page does pony boy help the kids out of the church? What is the y-intercept of a line that passes through the points (1,-7) and (5,-15)? You want to be able to withdraw $30,000 from your account each year for 15 years after you retire. If you expect to retire in 25 years and your account earns 6.4% interest while saving for retirement and 5.6% interest while retired:Round your answers to the nearest cent as needed.a) How much will you need to have when you retire?$ 448,704.35 (correct answer) b) How much will you need to deposit each month until retirement to achieve your retirement goals?c) How much did you deposit into you retirement account?d) How much did you receive in payments during retirement?e) How much of the money you received was interest? To compare the average amount of time that canadians and americans spend commuting, a researcher collects a sample of canadians and americans. The canadians spend an average of hours a week commuting, with a standard deviation hours. The mean and standard deviation for the sample of americans is hours and hours, respectively. The standard error of the difference of sample means is:. LMNP is a rectangle. Find the value of x and the length of each diagonal. LN=X AN MP=4x-18 please help me im horrible at spanish Read this sentence from paragraph 7 of The Problem That Has No Name and answer the question.Sometimes she blotted out the feeling with a tranquilizer.The author most likely uses the phrase blotted out to convey that the feeling was _____. The boundary where crust gives way to mantle is called the _______. A. Asthenosphere b. Mesosphere c. Mohorovicic discontinuity d. Vernian divide. did this webside is working? Read the passage from Hamlet, Act I, Scene iii. Hamlet:. But tell Why thy canonizd bones, hearsed in death, Have burst their cerements; why the sepulchre, Wherein we saw thee quietly inurnd,55 Hath opd his ponderous and marble jaws, To cast thee up again. What may this mean, That thou, dead corse, again in complete steel Revisitst thus the glimpses of the moon. Which phrases provide clues that sepulchre means "grave"? Check all that apply. Canonizd bones hearsed in death we saw thee ponderous and marble jaws the glimpses of the moon. what are quantum computers and it uses Which of the following equations represent a proportionalrelationship?Select two answers Evaluate 1/5y + 4/15 when y = 1/3 How are human persons integral parts of society? help pooo :(( how to tell if something is a strong or weak acid or base explain the different conditions that can result in hot and cold lahars, and explain how lahars change the earth's surface? -)1) Imagine you've been assigned to write a narrative essay about a time where you learned something from an unexpected situationWhich would be the BEST way to sequence the events of your story to develop your narrative?esA) Start with what you expected to happen, explain what was unexpected, then state what you learnedB) Start with was was unexpected, state what you learned, then write about what you expected to happen.Start with what you learned, state what was unexpected, then write about what you expected to happen.D) None of the choices represent a good sequence for this essay, as any sequence of events can work for a narrative essay if the writer just uses enough strongvocabulary words. Which is not a structure of comparative anatomy of organisms?. I need the answers for this please