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Internet Audience At the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that
z − u = 3(x − y) + 12
x + y = 50 + z + u
and x − y + z − u = 48.
How large was the audience of each of the four companies at the end of that year? Microsoft

Time Warner

Yahoo

Google

Respuesta :

MrRoyal

Answer:

Microsoft = 89.5 million

Time Warner = 77.5 million

Yahoo = 82.5 million

Google = 34.5 million

Step-by-step explanation:

Given

z − u = 3(x − y) + 12

x + y = 50 + z + u

x − y + z − u = 48.

From the question, we also understand that

u + x + y + z = 284

Required

Solve for u, x, y and z

Substitute 3(x - y) +12 for z - u in the third equation

x − y + z − u = 48.

(x - y) + 3(x - y) = 48

4(x - y) = 48

Divide both sides by 4.

x - y = 12

Make z + u the subject of formula in u + x + y + z = 284

z + u = 284 - (x + y)

Substitute 284 - (x + y) for z + u in the second equation

x + y = 50 + z + u

x + y = 50 + 284 - (x + y)

(x + y) + (x + y) = 50 + 284

2(x + y) = 334

Divide both sides by 2

x + y = 167

Make x the subject of formula

x = 167 - y

Substitute 167 - y for x in x - y = 12

167 - y - y = 12

167 - 2y = 12

-2y = 12 - 167

-2y = -155

2y = 155

y = 77.5

Solve for x in x = 167 - y

x = 167 - 77.5

x = 89.5

Recall that:

z − u = 3(x − y) + 12

z + u = 284 - (x + y)

Substitute the values of x and y in the above expressions.

z − u = 3(x − y) + 12

z - u = 3(89.5 - 77.5) + 12

z - u = 3(12) + 12

z - u = 36 + 12

z - u = 48

Make z the subject

z = 48 + u

Similarly,

z + u = 284 - (x + y)

z + u = 284 - (89.5 + 77.5)

z + u = 284 - 167

z + u = 117

Substitute 48 + u for z

48 + u + u = 117

48 + 2u = 117

2u = 117 - 48

2u = 69

u = 34.5

Substitute 34.5 for u in z = 48 + u

z = 48 + 34.5

z = 82.5

The size of audience of each of the four companies at the end of that year are;

Micro-soft = 89.5 million

Time Warner = 79.5 million

Yah oo = 34.5 million

Goo gle = 82.5 million

We are given the equations;

z − u = 3(x − y) + 12 ----(1)

x + y = 50 + z + u   ----(2)

x − y + z − u = 48    ----(3)  

Now, we are told that the combined 4 audience is 284 million users. Thus;

u + x + y + z = 284    ----(4)  

Put 3(x − y) + 12 for z - u in the eq 3 to get;

(x - y) + 3(x - y) = 48

x - y + 3x - 3y

4x - 4y = 48

Divide both sides by 4 to get;

x - y = 12   ----(5)

Make z + u the subject of formula in eq 4 to get;

z + u = 284 - (x + y)  ---(4b)

Put 284 - (x + y) for z + u in the eq 2;

x + y = 50 + 284 - (x + y)

x + y = 334 - x - y

Add x + y to both sides to get;

x + y + x + y = 334

2x + 2y = 334

Divide both sides by 2 to get;

x + y = 167 -----(6)

Add eq 5 to eq 6 to get;

2x = 167 + 12

2x = 179

x = 179/2

x = 89.5

Put 89.5 for x in eq 6 to get;

89.5 + y = 167

y = 167 - 89.5

y = 77.5

 

Put the values of x and y in eq(1) and eq(4b) to get;

z - u = 3(89.5 - 77.5) + 12

 z - u = 48  ---(7)

 

Also,

z + u = 284 - (89.5 + 77.5)

z + u = 117   ---(8)

Add eq 7 to eq 8 to get;

2z = 165

z = 165/2

z = 82.5

Put 82.5 for z in eq 8 to get;

82.5 + u = 117

u = 117 - 82.5

u = 34.5

Read more at; https://brainly.com/question/14526969

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