Question

At the end of a certain year, the four organizations ranking 5 through 8 in home Internet users in the United States were eBay, the U.S. Government, Amazon, and Lycos, with a combined audience of 112 million users. Taking x to be the eBay audience in millions, y the U.S. Government audience in millions, z the Amazon audience in millions, and u the Lycos audience in millions, it was observed that

y − z = z − u
x− y= 3(y − u) + 17
and x− y + z−u = 24.
How large was the audience of each of the four organizations at the end of that year?

Answer 1

The size of the audience of each group are;

Ebay audience x = 46 million

U. S. Government audience, y = 23 million

Amazon audience, u = 21 million

Lycos audience, z = 22 million

The steps used to find the size of the audience of the four organization can be presented as follows;

The system of equation by which the variables, u, x, y, and z can be found is presented as follows;

u + x + y + z = 112...(1)

y - z = z - u...(2)

x - y = 3·(y - u) + 17...(3)

x - y + z - u = 24...(4)

Equation (4) indicates;

x + z = 24 + y + u

u + x + y + z = 112, therefore;

u + y + 24 + y + u = 112

2·u + 2·y = 88

u + y = 88/2

u + y = 44

y - z = z - u, therefore;

y + u = z + z

y + u = 2·z

u + y = 2·z

u + y = 44

2·z = 44

z = 44/2

Lycos audience z = 22

x - y = 3·(y - u) + 17

3·(y - u) + 17 + z - u = 24

3·y - 3·u + 17 + 22 - u = 24

3·y - 4·u = 24 - 39

3·y - 4·u = -15

u + y = 44

4·u + 4·y = 176

3·y - 4·u + 4·u + 4·y = -15 + 176

7·y = 1161

y = 161/7

The U. S. Government audience, y = 23

u = 44 - 23

Amazon audience. u = 21

u + x + y + z = 112

x = 112 - (u + y + z)

x = 112 - (21 + 23 + 22)

Ebay audience is; x = 46