Can someone please solve them?

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

svetlana [45]

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!!

7 0

3 years ago

Start with k, add 2, multiply by 6, then subtract 8. Please answer its URGENT! needed NOW

adelina 88 [10]

The answer is 4 because k+2 would be 2 then times by 6 which is 12 then subtract 8 would be 4

3 0

2 years ago

se vendieron 144 boletos. 2 pesos por adulto y un peso por niño, si se gastaron 207 pesos cuantos boletos de adulto se vendieron

natulia [17]

Answer:

Se vendieron 81 boletos de niños y 63 boletos de adultos.

Step-by-step explanation:

La cantidad de boletos vendidos es igual a:

$144 = a + n$ (1)

En donde a es por adultos y n por niños

A su vez, el dinero gastado equivale:

$207 = 2*a + 1*n$ (2)

Resolviendo la ecuación (1) para a:

$a = 144 - n$ (3)

Introduciendo (3) en la ecuación (2) tenemos:

$207 = 2*(144 - n) + n$

$n = 81$

Ahora podemos calcular el numero de boletos de adultos vendidos introduciendo n en la ecuación (3):

$a = 144 - n = 144 - 81 = 63$

Entonces, se vendieron 81 boletos de niños y 63 boletos de adultos.

Espero que te sea de utilidad!

5 0

2 years ago

Tell whether the expression 3x^4 -5x +7 is a polynomial. If it is polynomial , find the degrees and determine whether it is a mo

ioda

Given:

The polynomial is:

$3x^4-5x+7$

To find:

The degrees and determine whether it is a monomial, binomial, or trinomial.

Solution:

We have,

$3x^4-5x+7$

The highest power of the variable x in the given polynomial is 4. So, the degree of the polynomial is 4.

Monomial: Polynomial with one term.

Binomial: Polynomial with two terms.

Trinomial: Polynomial with three terms.

In the given polynomial, we have three terms $3x^4,-5x,7$ . So, the given polynomial is trinomial.

Therefore, the degree of the polynomial is 4 and it is a trinomial.

5 0

2 years ago

Anna, Beth and Colleen are softball players. This season, Anne had 65 base hits in 160 at-bats. Beth batting average was 0.399,

zheka24 [161]

Answer:

Anne is the best hitter as she has the best hitting average of 0.406

Step-by-step explanation:

Anne hits 65 bases out of 160 at - bats.

Beth's betting average = 0.399

Collin's hit = 40%

Now, we need to convert all the three hitting rates into same parameters to compare them with each other.

Average hit rate of Anne = $\frac{\textrm{Total numberof base}}{\textrm{Total number of at - bats}}$

$= \frac{65}{160} = 0.406$

⇒The betting average of Anne = 0.406

Now, The hit - rate of Collin = 40%

Converting the percentage rate into decimal, we get the hit rate of Collin

= $\frac{40}{100} = 0.40$

Hence, we get that Hitting Average of :

Anne = 0.406, Beth = 0.3999 and Collin = 0.400

Hence, from the above data Anne is the best hitter as she has the best hitting average of 0.406.

6 0

3 years ago

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