A web hosting company charges each enterprise client a one-time fixed setup fee plus a con… — GMAT

A web hosting company charges each enterprise client a one-time fixed setup fee plus a constant monthly maintenance fee per server. A client operating $4$ servers pays a total of $\$1,100$ for the setup fee and the first $6$ months of server maintenance. A client operating $9$ servers pays a total of $\$1,850$ for the setup fee and the first $6$ months of server maintenance. What is the one-time fixed setup fee, in dollars?

Cevap: 500 dollars

Cevap

500

The fixed setup fee is

\$500

. Letting

S

represent the fixed setup fee and

M

represent the 6-month maintenance fee per server, the two given scenarios yield

S + 4M = 1100

and

S + 9M = 1850

. Subtracting the first equation from the second gives

5M = 750

, which simplifies to

M = 150

. Substituting

M = 150

into

S + 4(150) = 1100

gives

S + 600 = 1100

, so

S = 500

Adım Adım Çözüm

Define variables for the unknown fixed cost and per-server cost, and construct the system of linear equations.

Let

S

be the fixed setup fee in dollars and

M

be the 6-month maintenance fee per server in dollars. The equations are

S + 4M = 1100

and

S + 9M = 1850

Modeling the situational relationships as a linear system allows isolated solution of each unknown.

Subtract the two linear equations to eliminate the fixed fee

S

and solve for

M

5M = 750 \implies M = 150

Since the coefficient of

S

is 1 in both equations, elimination by subtraction directly isolates

M

Substitute the value of

M

back into the first equation to solve for

S

S + 4(150) = 1100 \implies S + 600 = 1100 \implies S = 500

Replacing

M

with 150 yields a linear equation in one variable for the setup fee.

Anahtar Kavram

Linear Equations in One and Two Variables

Tahmini Süre:1m 30s

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