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
ira [324]
3 years ago
6

There are some goats, cows, and sheep on a farm. 2/5 of the animals were goats. There are 3 times as many sheep as cows. If ther

e are 45 more goats than cows, how animals were there in the farm?
Mathematics
1 answer:
svetlana [45]3 years ago
7 0

Answer:

180

Step-by-step explanation:

First thing to do is to get all the animals in terms of cows, since that is our main unknown.  All the other animals' numbers are based on cows.  So let's call cows "x".  Then sheep is 3 times the number of cows, so sheep is 3x.  The number of goats is 45 more than the number of cows, so goats is x + 45.  Let's say, for the sake of ease, that the number of animals is "a".

Here's what we have so far:

# of animals: a

# of cows: x

# of sheep: 3x

# of goats: x + 45

We are told that 2/5 of the animals are goats.  In an equation, that is:

2/5 (animals) = goats, where the word "of" means to multiply, and the word "are" is the equals sign.  Filling in from our key above:

\frac{2}{5}a=x+45

That says that 2/5 of the animals are goats when goats is x + 45.

If 2/5 of the animals are goats, then 3/5 of the animals have to be cows and sheep.  In an algebraic equation:

\frac{3}{5}a=x + 3x.  

Let's go back to the first equation and get rid of the fraction by multiplying everything by 5.  When we do that we get

2a = 5(x + 45) so

2a = 5x + 225

Now let's get rid of the fraction in the second equation by multiplying everything by 5.  When we do that we get

3a = 5(x + 3x) or

3a = 5(4x) so

3a = 20x.  Solve that equation for a.

a=\frac{20}{3}x

Now that we have a in terms of x, we can sub that value in for a in the first equation to solve for x, the number of cows:

2(\frac{20}{3}x)=5x+225 and, simplifying:

\frac{40}{3}x=5x+225 and

\frac{40}{3}x-5x=225.  Get rid of the fraction here by multiplying everything by 3:

40x - 15x = 675 and

25x = 675 so

x = 27

That means that there are 27 cows.

Sheep is 3 times that, so there are 81 sheep.

Goats is 45 more than that, so there are 72 goats.

The total number of animals then is 27 + 81 + 72 which is 180.  Let's check that to see if the number of goats, 72, is 2/5 of 180.

\frac{2}{5}(180) = 72

So we got it!  Yay!  That was hard!!

You might be interested in
I'm awful at word problems someone please help
Lubov Fominskaja [6]

Your answer is B.

Flat fee is $250, so we cannot change this number.
585 - 250 = 335
335 (remaining cash) divided by 8 (price per student) = 41.875
Since we can't bring .8 of one student on the trip, we will round the number down to 41, because if we round up we will go over the budget of $585.

The maximum number of students a school can send is 41.
6 0
3 years ago
Read 2 more answers
Please help I need help
aliina [53]
It think the answer could quite possibly be 4
8 0
3 years ago
What does 0.14 x 60 equal?
blondinia [14]
It equals 8.4 

Hope this answers ur question
4 0
3 years ago
Read 2 more answers
What is 1873 divided by 0.93
Firlakuza [10]

Answer:

it is 2013.97849462

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

6 0
3 years ago
(ANSWER FOR FREE BRAINPOINTS!) (FIRST TO ANSWER GETS BAINLIEST) The local park has a rectangular swimming pool that measures 40
iren [92.7K]

Answer:

9 yards

Step-by-step explanation:

Since both pools are similar, therefore the ratio of their length and width would be equal. That is:

Length of the current swimming pool : length of the new swimming pool = width of the current swimming pool : width of the new swimming pool

Thus, we can set up a proportion as shown below:

Let the width of the new swimming pool be x.

40 : 24 = 15 : x

\frac{40}{24} = \frac{15}{x}

Cross multiply

40*x = 15*24

40x = 360

Divide both sides by 40

x = \frac{360}{40}

x = 9

The width of the new swimming that is smaller would be 9 yards.

4 0
2 years ago
Other questions:
  • How does Mr. Peters get to ask for three wishes?
    10·1 answer
  • Ali has a quarters, d dimes, and n nickels. He gets four more quarters. He gives away three
    7·1 answer
  • Twenty of the 25 students in Mrs. Thigpen’s class are we wearing sneakers. What is the fraction in simplest form?
    11·1 answer
  • Match the numerical expressions to their simplest forms
    12·2 answers
  • Please help!! need to pass this class!!
    13·1 answer
  • Solve the system of equations by elimination.<br> 2x - y + 3z=-1<br> x + 2y - 4z=-1<br> y – 2z=0
    11·1 answer
  • Hello! How've you been lately? Have you had some water today? Just checking up on y'all because why not and also I'm sort of bor
    8·2 answers
  • Need Help ASAP Will Mark Brainliest
    6·1 answer
  • What number is 1/10 of 8,000,000
    14·1 answer
  • How can you show your work for 8800 divided by 4
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!