A cloud computing infrastructure employs two types of processing nodes: Server-Type X and … — GMAT

A cloud computing infrastructure employs two types of processing nodes: Server-Type X and Server-Type Y. A configuration consisting of 3 Server-Type X nodes and 5 Server-Type Y nodes processes 4,100 data transactions per second. A second configuration consisting of 5 Server-Type X nodes and 2 Server-Type Y nodes processes 4,300 data transactions per second. Assuming each node of a given type operates at a constant rate, what is the processing capacity, in data transactions per second, of a single Server-Type X node?

Answer: 700 data transactions per second

Answer

700 data transactions per second

Let

x

be the capacity of Server-Type X and

y

be the capacity of Server-Type Y. The system

3x + 5y = 4100

and

5x + 2y = 4300

simplifies to

19x = 13300

after eliminating

y

, yielding

x = 700

Step-by-Step Solution

Set up the linear equations representing the two node configurations.

3x + 5y = 4100

and

5x + 2y = 4300

, where

x

and

y

represent the processing rates of Server-Type X and Server-Type Y, respectively.

Translating word problems into algebraic equations allows systematic solving for unknown rates.

Eliminate the variable

y

by multiplying the equations by appropriate constants.

6x + 10y = 8200

and

25x + 10y = 21500

Aligning the coefficients of

y

enables elimination through subtraction.

Subtract the first modified equation from the second and solve for

x

19x = 13300 \implies x = 700

Solving the single-variable equation yields the processing capacity for Server-Type X.

Key Concept

Solving simultaneous linear equations in two variables using elimination

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