MATH SOLVE

2 months ago

Q:
# 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) 5/6b) 1/5c) 1/6d) 1/7e) 1/24

Accepted Solution

A:

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 = 30Since 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]