Question

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

Answer 1

Answer:

$\dfrac{1}{7}$

is the fraction of sensors upgraded per unit.

Step-by-step explanation:

We are given the following in the question:

Let x be the number of upgraded sensors in one unit and y be the number of non-upgraded sensors in one unit.

Number of modular units = 30

Since some part of unit is upgraded and some are non-upgraded, then, we can write the equation:

$x + y = 1$

Number of non-upgraded sensors =

$\dfrac{1}{5}\times \text{Total number of upgraded sensors on the entire satellite}$

Thus, we can write the equation:

$y = \dfrac{30x}{5}\\\\y = 6x\\1-x = 6x\\\\x = \dfrac{1}{7}$

Fraction of sensors upgraded per unit =

$\dfrac{1}{7}$