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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

Finance Nov 13, 2020

At the end of a certain year, the four companies with the largest number of home Internet users in the United States were MicrosoftTime WarnerYahoo, 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 = 48 + z + u
and   x y + z u = 44.

How large was the audience of each of the four companies at the end of that year?

Microsoft=

Time Warner=

Yahoo=

Google=

Expert Solution

Given information

z-u = 3(x-y)+12------equation 1

x-y+z-u = 44---------------equation 2

when we substitue the value of equation 2 in equation 1

x-y +3(x-y)+12 = 44

x-y+3x-3y+12=44

x-y+3(x-y)=32

x-y+3x-3y=32

4x-4y=32

4(x-y)=32

x-y=8;

x=8+y or y=x-8----equatiion 3

when we substitute the value of x in the given information

x-y+z-u==44

y+8-y+z-u = 44

8+z-u=44

z= 36+u-------equation 4

substitute the value of equation 4 and equation 3 in the given information of x+y value

x+y=48+z+u

y+8+y=48+36+u+u

2y+8=84+2u

2y=76+2u

y=u+38------equation 5

substitute the equatiion 3 in the above equation 5

x-8=u+38

x=46+u-----equation 6

to find out the value of u substitute the equation 4, 5 and 6 in the given information of x+y+z+u=284

x+y+z+u=284

46+u+u+38+36+u+u=284

4u+120=284

4u=164

therefore u= 164/4=41

to find out the value of z; substitute the value of u in equation 4

z=36+u

z = 36+41

z = 77

to find out the value of x ; substitute the value of u in equation 6

x = 46+u

x = 46+41

x = 87

to find out the value of y ; susstitute the value of y in equation 5

y= u+38

y = 41.+38

y = 79

check x+y+z+u = 284

= 87+79+41+77

= 284

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