Acompany has a budget of $280,000 for computing equipment. tablets cost $500 each, laptops cost $2000 each, and servers cost $5000 each. the company needs 5 times as many tablets as laptops, and two times as many laptops as servers. set this problem up as a system of three linear equations, and use trial and error to determine the approximate number of each type of machine should be purchased.

The number of tablets  200

the number of laptops  40

and, the number of servers 20

Step-by-step explanation:

Let the number of tablets be 'x'

the number of laptops be 'y'

and, the number of servers be 'z'

According to the given question

Total budget = $280,000

Tablets cost = $500 each

laptops cost = $2000 each

servers cost = $5000 each

Thus,

500x + 2000y + 5000z = 280,000 ..............(1)

also,

x = 5y  ................(2)

and,

y = 2z  

or

z =   ............(3)

substituting y from 2 and 3 in equation 1,  we get

(500 × 5y) + (2000 × y) + (5000 × ) = 280,000

or

2500y + 2000y + 2500y = 280,000

or

7000y = 280,000

or

y = 40

substituting y in equation 2, we get

x = 5 × 40 = 200

substituting y in equation 3 we get

z =

or

z = 20

hence,

the number of tablets  200

the number of laptops  40

and, the number of servers 20