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

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

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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

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step-by-step explanation: