Find the unknown digit to make each statement true

A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from dairy I co

zubka84 [21]

Answer:

a) i The company should buy 40 gallons from dairy I and 60 gallons from dairy

ii) What is the maximum amount of butterfat? The total amount of butterfat from Diary I and Diary II = 3.12% + 1.93%

=5.05%

b.The excess capacity of dairy I is 10 gallons, and for dairy II it is 30 gallons.

Step-by-step explanation:

a. How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum amount of butterfat?

From the question, we are told that:

Milk from dairy I costs $2.40 per gallon, Milk from dairy II costs $0.80 per gallon.

Let's represent:

Number of gallons of Milk from dairy I = x

Number of gallons of Milk from dairy II = y

At most $144 is available for purchasing milk.

$2.40 × x + $0.80 × y = 144

2.40x + 0.80y = 144........ Equation 1

x + y = 100....... Equation 2

x = 100 - y

2.40(100 - y) + 0.80y = 144

240 - 2.4y + 0.80y = 144

-1.60y = 144 - 240

-1.6y = -96

y = -96/-1.6

y = 60

From Equation 2

x + y = 100....... Equation 2

x + 60 = 100

x = 100 - 60

x = 40

Therefore, since number of gallons of Milk from dairy I = x and number of gallons of Milk from dairy II = y

The company should buy 40 gallons from dairy I and 60 gallons from dairy

II. What is the maximum amount of butterfat?

From the question

Dairy I can supply at most 50 gallons averaging 3.9% butterfat,

50 gallons = 3.9% butterfat

40 gallons =

Cross Multiply

= 40 × 3.9/50

= 3.12%

Dairy II can supply at most 90 gallons averaging 2.9% butterfat.

90 gallons of milk = 2.9% butter fat

60 gallons of milk =

Cross Multiply

= 60 × 2.9%/90

=1.9333333333%

≈ 1.93%

The total amount of butterfat from Diary I and Diary II = 3.12% + 1.93%

=5.05%

b. The solution from part a leaves both dairy I and dairy II with excess capacity. Calculate the amount of additional milk each dairy could produce.

Excess capacity of Diary I =

50 gallons - 40 gallons = 10 gallons

Excess capacity of Diary II =

90 gallons - 60 gallons = 30 gallons

Therefore, the excess capacity of dairy I is 10 gallons, and for dairy II it is 30 gallons.

3 0

2 years ago

3 1/2 divided by 1/4

yuradex [85]

Answer:

Have a great day

Step-by-step explanation:

=3 1/2÷1/4

=7/2×4

=7×2

=14

5 0

2 years ago

Question is in attached file

Nonamiya [84]

The rate of the passenger train is 81.67 MPH and the rate of the freight train is 66.67 MPH.

<h3>What is a linear equation?</h3>

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

The distance traveled by passenger train = 245 miles

The distance traveled by freight train = 245 miles

The time takes for both trains is the same.

Let's suppose the rate of the passenger train is x and the rate of the freight train is y;

As we know,

Distance = speed×time

245/x = 200/y

200x = 245y

200x - 245y = 0 ..(1)

x = 15 + y ..(2)

Equations (1) and (2) represent the situation.

After solving equations (1) and (2):

$\rm x=\dfrac{245}{3}= 81.67\\\\\\\:y=\dfrac{200}{3}=66.67$

Thus, the rate of the passenger train is 81.67 MPH and the rate of the freight train is 66.67 MPH.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ1

5 0

1 year ago

Who was Novia scotias reform leader

qaws [65]

Step-by-step explanation:

Their leaders were Charles Tupper and Adams george Archibald

7 0

2 years ago

15) If the point (6, 3) is rotated 180° clockwise about

dalvyx [7]

Answer:

B. (-2, 15)

Step-by-step explanation:

Pretend that your fixed point [2, 9] is at the origin for now by translating it two units west then nine units south [0, 0]. Now, the same goes for [6, 3]. Translate it two units west then nine units south to get [4, -6]. Then, according to the 180°-rotation rule, you take the OPPOSITE of both the x-coordinate and y-coordinate:

[4, -6] → [-4, 6]

Now, that you have your rotated point, we have to shift EVERYTHING BACK to the way it was from when we shifted the fixed point of [2, 9] to the origin. We do that by translating everything in reverse order, which is 9 blocks north then 2 blocks east:

→ [0, 0] back to [2, 9]

Translation

→ [-4, 6] to the new coordinate of [-2, 15]

I am joyous to assist you anytime.

8 0

2 years ago