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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
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 | = | 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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