A telecommunications satellite utilizes two distinct signal amplifier modules, Module A an… — GMAT

A telecommunications satellite utilizes two distinct signal amplifier modules, Module A and Module B, to process high-frequency and low-frequency data streams. Each Module A processes $18\text{ Gbps}$ of high-frequency data and $12\text{ Gbps}$ of low-frequency data, consuming $150\text{ watts}$ of operational power. Each Module B processes $30\text{ Gbps}$ of high-frequency data and $6\text{ Gbps}$ of low-frequency data, consuming $180\text{ watts}$ of operational power. During a peak transmission test, the active modules processed a combined total of $354\text{ Gbps}$ of high-frequency data and $138\text{ Gbps}$ of low-frequency data. What is the total operational power, in watts, consumed by all the active modules during this test?

Answer: 2460 watts

Answer

The total operational power consumed by all active modules during the test is 2,460 watts.

By setting up a system of simultaneous equations representing the total high-frequency (

18a + 30b = 354

) and low-frequency (

12a + 6b = 138

) bandwidths, solving yields

a = 8

active Module A units and

b = 7

active Module B units. Substituting these module counts into the total power equation

150(8) + 180(7)

gives exactly 2,460 watts.

Step-by-Step Solution

Define variables for the unknown counts of modules.

Let

a

represent the number of Module A units and

b

represent the number of Module B units.

Establishing explicit variables allows representing the data throughput and power constraints as algebraic equations.

Formulate equations for high-frequency and low-frequency data streams based on total throughput.

High-frequency equation:

18a + 30b = 354

. Low-frequency equation:

12a + 6b = 138

Summing the data contributions from each module type gives the total processed bandwidth for each frequency band.

Solve the system of linear equations.

Simplifying the low-frequency equation yields

2a + b = 23 \implies b = 23 - 2a

. Substituting into the simplified high-frequency equation (

3a + 5b = 59

) gives

3a + 5(23 - 2a) = 59 \implies -7a = -56 \implies a = 8

. Substituting

a = 8

back into

b = 23 - 2(8)

gives

b = 7

Determining the exact number of active modules of each type is required before calculating overall energy usage.

Calculate the total power consumption.

Total Power =

150a + 180b = 150(8) + 180(7) = 1,200 + 1,260 = 2,460\text{ watts}

Multiplying the module counts by their respective wattage ratings yields the total operational power.

Key Concept

Solving systems of simultaneous linear equations with two unknowns and applying the solution to calculate a weighted linear total.

Estimated Time:2m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic