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

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

Solve for m.

m – 7/8 = 5

Write your answer as a fraction or as a whole or mixed number.

m = ____

Answers

Answer:

5 7/8

Step-by-step explanation:

Do the inverse operation.

5 + 7/8 = 5 7/8

Or, do this instead!

Add 7/8 to both sides of the equation. On the side before the equal sign, -78 and +78 cancel out, leaving m all by itself. Bring down the equals sign and we have m = 5 7/8!

Pls help with at least one and explain how u solved it so I can do the rest myself

Answers

Answer:

14. decrease

15. divide 59.95 by 40

16. increase

Which number line correctly shows –0.8 + 0.6?



A number line going from negative 1.6 to positive 1.6. An arrow goes from negative 0.8 to negative 0.2, and then backwards from 0 to negative 0.8.
A number line going from negative 1.6 to positive 1.6. An arrow goes from 0 to negative 0.8 and then from negative 0.8 to negative 1.4.
A number line going from negative 1.6 to positive 1.6. An arrow goes from 0 to 0.8 and then from 0.8 to 1.4.
A number line going from negative 1.6 to positive 1.6. An arrow goes from negative 0.6 to 0.2 and then from 0 to negative 0.6.
Mark this and return

Answers

Answer:

Step-by-step explanation:

Since -0.8 is located to the left of origin so when adding any value it will cause it to shift to the right. For example, add 0.1 to 0.8, we get a value of 0.7 shifting the arrow to the right, same goes for 0.2

-0.8 + 0.1 = -0.7

-0.8 + 0.2 = -0.6

-0.8 + 0.4 = -0.4

-0.8 + 0.6 = -0.2

In this way it ends at -0.2

Step-by-step explanation: I hope this helps:)

what is the perimeter of a triangle with 3 sides that measure 8 ft, 20 ft, 12 ft

Answers

Answer:

40 ft

Step-by-step explanation:

Perimeter is the sum of all 3 sides of a triangle.

For this particular triangle, add 8+20+12:

40

Answer:

40ft

Step-by-step explanation:

to find perimeter, you have to add up all the sides.

8ft+20ft+12ft+40ft

How is the product of 4 and 2 shown using integer tiles?
4 positive tiles and 2 positive tiles.
4 negative tiles and 2 negative tiles.
4 sets of 2 positive tiles.
4 sets of 2 negative tiles.

Answers

Answer:

4 negative tiles and negative tiles

A diver descends to a depth of –25.6 feet relative to sea level. How many feet must the diver ascend to reach sea level?
0.6 feet
25 feet
25.6 feet
256 feet

Answers

The answer is 25.6 feet.

Hope this helps

Which of the following expressions is equal to P/17

Answers

Answer:

a and b would work in my opinion because it doesn't say in which specific order.

Answer:

the answer is b

Step-by-step explanation:

im sorry if it was wrong

associative property or commutative property, or identity property or zero property

Answers

a. Commutative Property
b. Zero Property
c. Identity Property
d. Associative Property
a.) commutative property
b.) zero property
c.) identity property
d.) associative property

True or False? The energy in a pendulum converts kinetic energy to potential energy, and then back again.

Answers

the answer to this question is true
the correct answer is “true”

What is the perimeter of a rectangle with a length of 15 ft and a width of 32 ft?


A. 47 ft
B. 55 ft
C. 94 ft
D. 480 ft

Answers

Answer:

C) 94 ft

Step-by-step explanation:

The perimeter of a rectangle's formula is:

[tex]P = 2l + 2w / P = 2(l+w)[/tex]

I will use the second formula.

We are given the length of 15ft and a width of 32 ft.

[tex]P = 2(15 + 32)\\\rule{150}{0.5}\\P = 2(47)\\\\P = \boxed{94}[/tex]

The answer should be C.

Hope this helps.

Answer:

C. 94 ft.

Step-by-step explanation:

15*2=30 to find the length32*2=64 to find the width30+64=94 to find the perimeterTherefore, the answer is 94 ft.

what is the answer 4.3 x .8

Answers

Answer:

The answer is 3.44

Step-by-step explanation:

4.3 × 0.8 = 3.44

The answer is 3.44

-TheUnknownScientist 72

Answer:

3.44

Step-by-step explanation:

How can you tell when a rate is a unit rate?


Each of the numbers in the rate are single digit numbers.
Each of the numbers in the rate are single digit numbers.

It has a label.
It has a label.

It has a numerator of 1.
It has a numerator of 1.

It has a denominator of 1.
It has a denominator of 1.

Answers

Answer:

It has a numerator of 1

It has the numerator if 1, hope I helped :)


Minh and Mikayla are selling wrapping paper for a school fund-raiser. Customers can
buy either packages of folded paper or rolls of paper. Minh sold 6 rolls of paper and 2
packages of folded paper for a total of $44. Mikayla sold 3 rolls of paper and 9 packages
of folded paper for a total of $54. How much does each roll cost? How much does each
package of folded paper cost?

Answers

Answer:

Let x=rolls of paper,y=folded paper:

6x+2y=44

3x+9y=54

-------

6x+2y=44

6x+18y=108

16y=108-44=64

y=4

x=6

Thus, a roll of paper cost $6,folded paper was $4 each

Step-by-step explanation:

· A ball is dropped from a height of 256 feet. After it hits the ground, it rebounds to a height that is 75% of its previous maximum height. Use proportional reasoning to complete the table. Bounce 1 2 4 3 Maximum Height (ft) 256 Height of Bounce (ft)​

Answers

Answer:

The answer is 192 ft. :D

Step-by-step explanation:

PLEASE mark me brainliest! :)

I will give brainliest to whoever answers first

Answers

Answer:u need to guess bro

Step-by-step explanation:

Help plz:

14. Factor the following:
e. q^2 - 7q + 12
f. r^2 + 13r + 12
g. x^2 - x - 20
h. y^2 + 5y + 6

Answers

Answer:

e. (q-3)(q-4)

f. (r+1)(r+12)

g. (x-5)(x+4)

h. (y+2)(y+3)

please help me with my math problems

Answers

Answer:

a yes

byes

and that was it your answer

11.50 + 1.15x = 12.65
11.50 - 11.50 + 1.15x = 12.65 - 11.50

➗ 1.15x = 1.15 ➗ what does x equal? Please explain in great detail how you figured this out also replace the = with the proper inequality sign and explain how you did that as well.

Answers

Answer: the answer is x= 1

Step-by-step explanation:

So we are dealing with 11.50 - 11.50 + 1.15x = 12.65 - 11.50

our first step is Simplify both sides of the equation so:

11.5 + -11.50 + 1.15x = 12.65 + -11.50 turns into:

(1.15x) + (11.5+ -11.5)= (12.65 + -11.5)

**we know 11.5 + -11.5 will cancel each other since they are opposite**

so it will be 1.15x= 1.15

now the very last step is to divide 1.15x on both sides which gives us 1

X=1 I hope it helps but I’m sorry if it’s wrong

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

Please answer like this:
1) -insert answer-
2) -insert answer-

Answers

Answer:

  1) 2^9 = 512

  2) 2^(3t) = 2^6 for t=2

Step-by-step explanation:

1) An exponent is used to signify repeated multiplication. Here, the factor 2 is repeated 9 times, so the expression can be written using an exponent as ...

  2^9

Using any of a variety of means, the value of this expression can be found to be ...

  2^9 = 512

__

2) Assuming the bacteria reproduce by multiplying by some factor in a given time, we can divide the original expression into 3 parts:

  (2×2×2) × (2×2×2) × (2×2×2)

If this represents the number after 3 hours, then the number after 2 hours is expected to be ...

  (2×2×2) × (2×2×2) = 2^6

That is, there will be (2 h)/(3 h) = 2/3 times as many multiplications by a factor of 2. (2/3)(9) = 6 will be the exponent for the number after 2 hours.

1. 2^9 = 512
2. as you can split up the fact in 3 hours it is 2^9 to find out one hour (divide by 3) which is 2^3 so we would just multiply it by 2 which equals 2^6

Answer the following questions.

Answers

Answer:

Thanks for the questions

Thank you so much!!

!!please help me quick!!
find the equation of the line.
y=__x+__

Answers

Y= 3x + 3. Use rise (how many it goes up or down) and divide it by run (how many it goes left or right) that number is your slope (aka M/ the number that goes with x. The number without the x attached is just where the line crosses the y axis
Y=3x+3 use rise over run and the y intercept is y

Im so lost i dont get it

Answers

X always = 1
9-1x<-11

Which means
X>20 is your answer !

plz help meeeeeeeeeeeeee

Answers

after 6 weeks: 48kg
after 12 weeks: 21kg
w=15
function rule: r=2
I have no idea… sorry!

Min saved 334 pennies. Rami saved 6 times as many pennies as Min.

How many pennies did Rami save?



??pennies

Answers

Answer:

2004

Step-by-step explanation:

334*6=2,004



you have too take 334 and times that by 6 , that should give you 2,004 :)
i hoped i explained it okay, have a nice day !

As a scuba diver dives deeper and deeper into the ocean, the pressure of the water on his body steadily increases. The pressure at the surface of the water is 14.7 pounds per square inch (psi). The pressure increases at a rate of 0.445 psi for each foot you descend.

Answers

Answer:

domain is the values in x axis and the range is the value in y axis

Miss Riley's class has 24 students. She has the students in groups. Each group can have no more than 5 students. if every student has to be in groups how many does she have left?

Answers

Answer:

if there can be no more than 5 students, then anything less than 5 students will suffice. However we don’t want any left over ones cause we don’t want that one kid sitting alone during lunch so we can simply put 4 into each group.

Step-by-step explanation:

Hope this helped :DDD

Answer:

6 groups, 4 students in each one

Step-by-step explanation:

The factors of 24 include 6 and 4

That means that you can break 24 into those numbers

You are able to put the students up into groups of 6, with 4 students in each

However, you cannot place the students into groups of 4 (with 6 students in each) because no more than 5 students are allowed in each group

Help me please I dont get it

Answers

Answer:

x>10

Step-by-step explanation:

I hope it helps. Please let me know.

Answer:

2.5x > 25

Step-by-step explanation:

1. 10 + 2.5x > 35

2. 10 + 2.5x - 10 > 35 - 10 (Subtracting 10 from both sides)

3. 2.5x +10 - 10 > 35 - 10 (Group like terms)

4. 2.5x > 35 - 10 (Simplify the arithmetic)

5. 2.5x > 25

did I get this right please help me?

Answers

3,200 x 3.28 = 10,496.. so yes
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