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

Respuesta :

Answer:

[tex]\dfrac{1}{7}[/tex]

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:

[tex]x + y = 1[/tex]

Number of non-upgraded sensors =

[tex]\dfrac{1}{5}\times \text{Total number of upgraded sensors on the entire satellite}[/tex]

Thus, we can write the equation:

[tex]y = \dfrac{30x}{5}\\\\y = 6x\\1-x = 6x\\\\x = \dfrac{1}{7}[/tex]

Fraction of sensors upgraded per unit =

[tex]\dfrac{1}{7}[/tex]