A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?

a) 5/6

b) 1/5

c) 1/6

d) 1/7

e) 1/24

1/7 (option d) of the sensors on the satellite have been upgraded

Step-by-step explanation:

Each unit contains the same number of non-upgraded sensors

number of non-upgraded sensors for each module (nus)

total number of upgraded sensors on the satellite (tus)

satellite is composed of 30 modular units

total number of non-upgraded sensors on the satellite (tnus):

tnus=30*nus

total number of sensors on the satellite (ts):

ts=tnus+tus = 30*nus + tus (I)

The number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite

nus = (1/5) * tus

tus = 5 * nus (II)

Fraction of the sensors on the satellite have been upgraded (FU):

FU = tus/ts

Using I and II

FU = (5 * nus) / (30*nus + tus)

FU = (5 * nus) / (30*nus + 5 * nus)

FU = (5 * nus) / (35*nus)

FU = 1/7

1/7 (option d) of the sensors on the satellite have been upgraded