Problem Solving

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)1/2

Since we're asked to find a certain FRACTION, we can plug in some nice values that meet the given conditions.

Let's say that there's a TOTAL of 5 upgraded sensors on the entire satellite

the number of non-upgraded sensors on one modular unit is 1/5 the TOTAL number of upgraded sensors on the entire satellite
So, the number of non-upgraded sensors on EACH modular unit = (1/5)(5) = 1.

Since there are 30 modular units altogether, the TOTAL number of non-upgraded sensors = (30)(1) = 30.

So, the TOTAL number of sensors = (number of non-upgrades) + (number of upgraded)
= 30 + 5
= 35

What fraction of the sensors on the satellite have been upgraded?
= 5/35
= [spoiler]1/7[/spoiler]
= D

Cheers,
Brent