A technology company purchased a total of 35 computers for its new office, consisting of s… — GMAT

A technology company purchased a total of $35$ computers for its new office, consisting of standard desktop units costing $\$800$ each and high-performance workstation units costing $\$1,400$ each. If the total expenditure for all $35$ computers was $\$34,000$ , how many standard desktop units did the company purchase?

Cevap: 25 desktop units

Cevap

The company purchased 25 standard desktop units.

Let

x

be the number of standard desktop units and

y

be the number of workstation units. The situation yields two equations:

x + y = 35

and

800x + 1400y = 34000

. Simplifying the second equation gives

4x + 7y = 170

. Multiplying the first equation by

7

gives

7x + 7y = 245

. Subtracting the simplified cost equation from this product yields

3x = 75

, so

x = 25

Adım Adım Çözüm

Define variables and establish equations from the problem statement.

System of equations:

x + y = 35

and

800x + 1400y = 34000

, where

x

represents standard desktop units and

y

represents workstation units.

Linear systems represent total quantity and total cost constraints simultaneously.

Simplify the linear cost equation by dividing by the greatest common divisor (

200

Simplified equation:

4x + 7y = 170

Simplifying coefficients reduces arithmetic complexity and potential errors.

Solve for

x

using substitution or elimination.

-3x = -75 \implies x = 25

Isolating

x

directly calculates the required count of standard desktop units.

Anahtar Kavram

Solving a system of two linear equations in two variables using substitution or elimination

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