A hardware manufacturer produces two models of enterprise servers: Server X and Server Y. … — GMAT

A hardware manufacturer produces two models of enterprise servers: Server X and Server Y. Each Server X requires $3$ processors of Type A and $2$ processors of Type B. Each Server Y requires $2$ processors of Type A and $5$ processors of Type B. In a given production run, the manufacturer assembled a total of $40$ servers using exactly $115$ processors of Type A. What is the total number of Type B processors used in this production run?

Answer: 95 processors

Answer

The total number of Type B processors used in the production run is 95.

By representing the count of Server X models as

x

and Server Y models as

y

, the given conditions yield two equations:

x + y = 40

and

3x + 2y = 115

. Solving this system gives

x = 35

and

y = 5

. Substituting these values into the expression for Type B processors (

2x + 5y

) produces

2(35) + 5(5) = 70 + 25 = 95

Step-by-Step Solution

Define variables and establish equations for server totals and Type A processor usage.

x + y = 40

and

3x + 2y = 115

, where

x

is Server X count and

y

is Server Y count.

Word problems require translating relationships into algebraic linear equations.

Solve the system of equations for

x

and

y

using substitution.

x = 35

Server X models and

y = 5

Server Y models.

Finding the specific quantities of each server model is required to compute total Type B processors.

Substitute

x = 35

and

y = 5

into the expression for Type B processors (

2x + 5y

2(35) + 5(5) = 70 + 25 = 95

Determines the target unknown value requested in the problem stem.

Key Concept

Modeling word problems using systems of linear equations in two variables.

Estimated Time:2m 0s

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